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Accepted by: Zied Babai Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue, we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works. [ABSTRACT FROM AUTHOR]

This article examines the disparities between tuberculosis burden estimates provided by the World Health Organization (WHO) and the Institute for Health Metrics and Evaluation (IHME). The authors emphasize the importance of clearer explanations and reproducibility of IHME's methods. They suggest enhancing comparisons and dialogue between IHME and WHO to better understand the differences in data and methodologies. The article also proposes considering method changes to incorporate country-specific data and addressing inconsistencies in epidemiological patterns. Additionally, the authors recommend exploring statistical smoothing in the estimates and utilizing covariates to capture changes in TB programs. The article further discusses the use of projection estimates by IHME for predicting future disease burden, particularly for TB. The authors recommend that IHME take into account programmatic changes for TB in their methodology and emphasize the need for stronger explanations of methods, comparisons, and dialogue with WHO, as well as improved communication with stakeholders. While acknowledging the value of both IHME and WHO estimates, the authors identify areas for improvement. [Extracted from the article]

Reasonable parametrizations of the current Hubble data set of the expansion rate of our homogeneous and isotropic universe, after suitable smoothing of these data, strongly suggest that the area of the apparent horizon increases irrespective of whether the spatial curvature of the metric is open, flat, or closed. Put in another way, any sign of the spatial curvature appears consistent with the second law of thermodynamics. [ABSTRACT FROM AUTHOR]

Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as componentwise inference for multivariate data naturally performs feature selection, subsetwise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p‐values of hypothesis tests performed on pointwise evaluations of functional data are suitably adjusted for providing control of the familywise error rate (FWER) over a family of subsets of the domain. We show that several state‐of‐the‐art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined thresholdwise testing, in which the family of subsets is instead built in a data‐driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples and compare their performance with other existing methods. [ABSTRACT FROM AUTHOR]

Earthquake source inversion, which estimates the heterogeneous slip distribution on fault from geophysical data, is a fundamental technique for estimating earthquake rupture process and obtaining information about the physics of fault rupture. Source inversion requires the spatial discretization of fault, which can be performed uniformly and non-uniformly. Uniform fault discretization is a conventional approach that requires smoothing and/or non-negative constraints of slips as prior information to obtain a stable and reliable solution; however, the combination of uniform discretization and these prior constraints may distort a source-inversion solution. As a non-uniform discretization approach, source inversion using a trans-dimensional inversion approach has recently attracted attention. To study the effect of fault discretization on geodetic source inversion, through the analysis of geodetic data on the 2015 Gorkha, Nepal, earthquake and synthetic tests, we investigated what kind of solution the conventional source inversion with uniform discretization and the trans-dimensional source inversion provide and what kind of uncertainty their solutions have. We found that the combination of uniform discretization and non-negative constraint led to excessively smooth solutions with poor data fit. Even without using the non-negative constraint, the conventional inversion with uniform discretization provided distorted and sometimes overfitted solutions, which could not be identified based on uncertainty information. In contrast, the trans-dimensional source inversion provided reasonable solutions composed only of meaningful slips, which were required to explain the data. We also found that uncertainty information depends on the source-inversion method; consequently, the evaluation of method-induced uncertainty is difficult. This suggests that we look at earthquake ruptures through the lens of source inversion with inherent method-dependent bias. [ABSTRACT FROM AUTHOR]

Electroencephalography (EEG) is a noninvasive neuroimaging modality that captures electrical brain activity many times per second. We seek to estimate power spectra from EEG data that ware gathered for 557 adolescent twin pairs through the Minnesota Twin Family Study (MTFS). Typically, spectral analysis methods treat time series from each subject separately, and independent spectral densities are fit to each time series. Since the EEG data were collected on twins, it is reasonable to assume that the time series have similar underlying characteristics, so borrowing information across subjects can significantly improve estimation. We propose a Nested Bernstein Dirichlet prior model to estimate the power spectrum of the EEG signal for each subject by smoothing periodograms within and across subjects while requiring minimal user input to tuning parameters. Furthermore, we leverage the MTFS twin study design to estimate the heritability of EEG power spectra with the hopes of establishing new endophenotypes. Through simulation studies designed to mimic the MTFS, we show our method out‐performs a set of other popular methods. [ABSTRACT FROM AUTHOR]

We generalise a result of Bykovskii to the Gaussian integers and prove an asymptotic formula for the prime geodesic theorem in short intervals on the Picard manifold. Previous works show that individually the remainder is bounded by |$O(X^{13/8+\epsilon })$| and |$O(X^{3/2+\theta +\epsilon })$|⁠ , where |$\theta$| is the subconvexity exponent for quadratic Dirichlet |$L$| -functions over |$\mathbb{Q}(i)$|⁠. By combining arithmetic methods with estimates for a spectral exponential sum and a smooth explicit formula, we obtain an improvement for both of these exponents. Moreover, by assuming two standard conjectures on |$L$| -functions, we show that it is possible to reduce the exponent below the barrier |$3/2$| and get |$O(X^{34/23+\epsilon })$| conditionally. We also demonstrate a dependence of the remainder in the short interval estimate on the classical Gauss circle problem for shifted centres. [ABSTRACT FROM AUTHOR]

The high dynamic range between contaminating foreground emission and the fluctuating 21 cm brightness temperature field is one of the most problematic characteristics of 21 cm intensity mapping data. While these components would ordinarily have distinctive frequency spectra, making it relatively easy to separate them, instrumental effects and calibration errors further complicate matters by modulating and mixing them together. A popular class of foreground cleaning method are unsupervised techniques related to principal component analysis (PCA), which exploit the different shapes and amplitudes of each component's contribution to the covariance of the data in order to segregate the signals. These methods have been shown to be effective at removing foregrounds, while also unavoidably filtering out some of the 21 cm signal too. In this paper we examine, for the first time in the context of 21 cm intensity mapping, a generalized method called Kernel PCA, which instead operates on the covariance of non-linear transformations of the data. This allows more flexible functional bases to be constructed, in principle allowing a cleaner separation between foregrounds and the 21 cm signal to be found. We show that Kernel PCA is effective when applied to simulated single-dish (auto-correlation) 21 cm data under a variety of assumptions about foregrounds models, instrumental effects etc. It presents a different set of behaviours to PCA, e.g. in terms of sensitivity to the data resolution and smoothing scale, outperforming it on intermediate to large scales in most scenarios. [ABSTRACT FROM AUTHOR]

In this paper we introduce several geometric flows that evolve primarily non-degenerate 2-forms, with the motivation to develop a geometric flow to approach the existence of the symplectic forms on a compact manifold that supports a non-degenerate 2-form. In particular, we introduce |$\mathrm{d}^{\ast }\mathrm{d}$| -flow and |$\mathrm{d}^{\ast }\mathrm{d}$| -Ricci flow for a compatible pair |$(\omega , J)$| of an almost Hermitian structure. We prove the short time existence and uniqueness of these flows with smooth initial data, and give some examples of long time existence and convergence. [ABSTRACT FROM AUTHOR]

Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state‐of‐the‐art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change‐point models or Gaussian process priors. Change‐point models suffer from computational issues when the number of change‐points is unknown and needs to be estimated. Gaussian process‐based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log‐transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change‐point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]

Microseismic data are usually of low signal-to-noise ratio (SNR), which makes it difficult to utilize the microseismic waveforms for imaging and inversion. We develop a useful denoising algorithm based on a non-stationary least-squares decomposition model to enhance the quality of microseismic signals. The microseismic signals are assumed to be represented by a superposition of several smoothly variable components. We construct a least-squares inverse problem to solve for the the smooth components. We constrain the least-squares inversion via both time and space constraints. The temporal smoothness constraint is applied to ensure the stability when calculating the non-stationary autoregression coefficients. The space-smoothness constraint is applied to extract the spatial correlation among multichannel microseismic traces. The new algorithm is validated via several synthetic and real microseismic data and are proved to be effective. Comparison with the state-of-the-art algorithms demonstrates that the proposed method is more powerful in suppressing random noise of a wide range of levels than its competing methods. [ABSTRACT FROM AUTHOR]

It is common for firms to forecast stationary demand using simple exponential smoothing (SES) due to the ease of computation and understanding of the methodology. We consider a retailer who observes autoregressive moving average (ARMA) demand but for the sake of convenience, uses the widely available SES method to forecast its demand. This creates a potential disconnect between the true mechanism generating demand and the forecasting methodology. We show that the supplier, given a sufficiently long history of the retailer's orders, is always able to recover the retailer's true shocks, and in addition is able to infer the true ARMA model generating the retailer's demand process if the retailer shares its exponential smoothing parameter. We further prove that under these assumptions, the supplier is then able to infer the retailer's demand as well. Thus, the supplier is in possession of expertise that would benefit the retailer. However, as a result of the supplier sharing its forecasting expertise, we demonstrate that the demand the supplier will face can have a smaller or larger mean squared forecast error than when the retailer uses the suboptimal SES forecast. In addition, we show that if the supplier provides its forecasting expertise to the retailer, there may be value in the retailer sharing its demand with the supplier. We also perform a simulation study for a special case of an AR(1) demand process and demonstrate that as the sample size of data increases, the difference of mean squared errors between the supplier's estimations of the retailer's demand shocks and the retailer's true demand shocks converges to zero. [ABSTRACT FROM AUTHOR]

In this paper, new neural network (NN) methods are proposed to forecast intermittent demand and we empirically study their performance as compared to parametric and non-parametric forecasting methods proposed in the literature. The empirical investigation uses demand data for 5,135 spare parts for the fleet of aircrafts of an airline company. Three parametric benchmark methods are examined: single exponential smoothing (SES), Croston's method and Syntetos–Boylan approximation, along with two bootstrapping methods: Willemain's method and Zhou and Viswanathan's method. The benchmark NN method considered in this paper is that proposed by Gutierrez et al. (2008) The paper shows the outperformance of SES and the NN methods for (a) their forecast accuracy and (b) their inventory efficiency (trade-off between holding volumes and backordering volumes) when compared to the other methods. Moreover, among the NN methods, a new proposed method is shown to be better than that proposed by Gutierrez et al. in terms of forecast accuracy and inventory efficiency. [ABSTRACT FROM AUTHOR]

Motivation Improved DNA technology has made it practical to estimate single-nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth- and development-related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty. Results We introduce a completely tuning-free Bayesian Gaussian process (GP)-based approach for estimating dynamic variance components and heritability as their function. For parameter estimation, we use a modern Markov Chain Monte Carlo method which allows full uncertainty quantification. Several datasets are analysed and our results clearly illustrate that the 95% credible intervals of the proposed joint estimation method (which 'borrows strength' from adjacent time points) are significantly narrower than of a two-stage baseline method that first estimates the variance components at each time point independently and then performs smoothing. We compare the method with a random regression model using MTG2 and BLUPF90 software and quantitative measures indicate superior performance of our method. Results are presented for simulated and real data with up to 1000 time points. Finally, we demonstrate scalability of the proposed method for simulated data with tens of thousands of individuals. Availability and implementation The C++ implementation dynBGP and simulated data are available in GitHub: https://github.com/aarjas/dynBGP. The programmes can be run in R. Real datasets are available in QTL archive: https://phenome.jax.org/centers/QTLA. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

A scenario for the formation of the bi-modality in the chemical space [α/Fe] versus [Fe/H] of the Milky Way was recently proposed in which α-enhanced stars are produced early and quickly in clumps. Besides accelerating the enrichment of the medium with α-elements, these clumps scatter the old stars, converting in-plane to vertical motion, forming a geometric thick disc. In this paper, by means of a detailed analysis of the data from smooth particle hydrodynamical simulations, we investigate the geometric properties (in particular of the chemical thick disc) produced in this scenario. For mono-age populations we show that the surface radial density profiles of high-[α/Fe] stars are well described by single exponentials, while that of low-[α/Fe] stars require broken exponentials. This break is sharp for young populations and broadens for older ones. The position of the break does not depend significantly on age. The vertical density profiles of mono-age populations are characterized by single exponentials, which flare significantly for low-[α/Fe] stars but only weakly (or not at all) for high-[α/Fe] stars. For low-[α/Fe] stars, the flaring level decreases with age, while for high-[α/Fe] stars it weakly increases with age (although with large uncertainties). All these properties are in agreement with observational results recently reported for the Milky Way, making this a plausible scenario for the formation of the Galactic thick disc. [ABSTRACT FROM AUTHOR]

An optimal control problem for a linearized fluid–structure interaction model with a delay term in the structural damping is analyzed. A distributed control acting on the fluid domain, structure domain or both is considered. The necessary optimality conditions are derived both for rough and smooth initial data. A parabolic regularization of the problem and its convergence are investigated. Finite element discretization for the regularized problem and error estimates are provided. Piecewise linear elements with bubble functions for the fluid and a discontinuous Galerkin scheme for the spatial and temporal discretizations are utilized respectively. Numerical experiments illustrating the theoretical results are given. [ABSTRACT FROM AUTHOR]

We consider linear finite elements to approximate the elasticity equations with unilateral contact boundary conditions, in a bounded two- or three-dimensional domain with curved and smooth boundary. We use the penalty method to weakly impose these boundary conditions. We establish an error estimate in the energy norm with respect to the mesh size |$h$| and the penalty parameter |$\varepsilon $|⁠. Assuming |$\boldsymbol{H}^{\frac{3}{2}+\nu }\left (\varOmega \right)$| regularity of the solution, |$0 < \nu \leq \frac{1}{2}$|⁠ , we obtain an |$\mathcal{O}\,(h^{\frac{1}{2}+\nu } + \varepsilon ^{\frac{1}{2}+\nu })$| convergence rate. Therefore, if the penalty parameter is chosen as |$\varepsilon (h) := ch^{\theta }$| with |$0 < \theta \leq 1$|⁠ , we obtain an |$\mathcal{O}\,(h^{\theta (\frac{1}{2}+\nu)})$| convergence rate. Thus, the optimal linear convergence rate is obtained when |$\varepsilon $| behaves like |$h$| (that is, |$\theta = 1$|⁠) and |$\nu = \frac{1}{2}$|⁠. We present a numerical example to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Microseismic data are usually of low signal-to-noise ratio (SNR), which makes it difficult to utilize the microseismic waveforms for imaging and inversion. We develop a useful denoising algorithm based on a non-stationary least-squares decomposition model to enhance the quality of microseismic signals. The microseismic signals are assumed to be represented by a superposition of several smoothly variable components. We construct a least-squares inverse problem to solve for the the smooth components. We constrain the least-squares inversion via both time and space constraints. The temporal smoothness constraint is applied to ensure the stability when calculating the non-stationary autoregression coefficients. The space-smoothness constraint is applied to extract the spatial correlation among multichannel microseismic traces. The new algorithm is validated via several synthetic and real microseismic data and are proved to be effective. Comparison with the state-of-the-art algorithms demonstrates that the proposed method is more powerful in suppressing random noise of a wide range of levels than its competing methods. [ABSTRACT FROM AUTHOR]

Drawing inferences for high‐dimensional models is challenging as regular asymptotic theories are not applicable. This article proposes a new framework of simultaneous estimation and inferences for high‐dimensional linear models. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to low‐dimensional least squares estimations. The procedure, termed as Selection‐assisted Partial Regression and Smoothing (SPARES), utilizes data splitting along with variable selection and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a nonparametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with the de‐biased LASSO estimators, a major competitor. We apply the method to analyze two genomic datasets and obtain biologically meaningful results. [ABSTRACT FROM AUTHOR]

We investigate how the spectral properties of atomic (H i) and molecular (H2) gas, traced by CO(2−1) , are related in M33 on 80 pc scales. We find the H i   and CO(2−1)  velocity at peak intensity to be highly correlated, consistent with previous studies. By stacking spectra aligned to the velocity of H i  peak intensity, we find that the CO  line width (σHWHM = 4.6 ± 0.9  |${\rm km\, s^{-1}}$|  ; σHWHM is the effective Gaussian width) is consistently smaller than the H i  line width (σHWHM = 6.6 ± 0.1  |${\rm km\, s^{-1}}$|⁠), with a ratio of ∼0.7, in agreement with Druard et al. The ratio of the line widths remains less than unity when the data are smoothed to a coarser spatial resolution. In other nearby galaxies, this line width ratio is close to unity which has been used as evidence for a thick, diffuse molecular disc that is distinct from the thin molecular disc dominated by molecular clouds. The smaller line width ratio found here suggests that M33 has a marginal thick molecular disc. From modelling individual lines of sight, we recover a strong correlation between H i  and CO line widths when only the H i  located closest to the CO component is considered. The median line width ratio of the line-of-sight line widths is 0.56 ± 0.01. There is substantial scatter in the H i  –CO(2−1) line width relation, larger than the uncertainties, that results from regional variations on <500 pc scales, and there is no significant trend in the line widths, or their ratios, with galactocentric radius. These regional line width variations may be a useful probe of changes in the local cloud environment or the evolutionary state of molecular clouds. [ABSTRACT FROM AUTHOR]

Summary: Clinical practice may be enhanced by use of person‐level information that could guide treatment choice and lead to better outcomes for both treated individuals and for the population. The scientific challenge is to identify and validate those factors that can reliably be used to target treatment, and to accurately quantify the expected treatment benefit as a function of candidate markers. Our proposal is to explicitly focus on smooth non‐parametric evaluation of a canonical single index score that estimates the expected treatment benefit associated with patient characteristics. Our methods intentionally decouple the model used to generate the treatment benefit score from the methods that are adopted to evaluate the performance of the resulting single index score. We are motivated by the practical issue that model performance can not realistically be evaluated for every specific covariate value due to intrinsic sparseness. However, direct validation of a scalar treatment benefit score obtained through model‐based dimension reduction is feasible, and we believe should be the focus of validation efforts. We also show that the canonical single index treatment benefit score can be used for selecting subsets of patients with enriched expected treatment response since patients can be easily ordered and grouped based on the scalar score. Our biomedical motivation comes from a recent randomized trial of steroid injections for low back pain where baseline clinical and imaging data are candidate measures for guiding therapeutic choice. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical models produce shrinkage estimators that can be used as the basis for integrating supplementary data into the analysis of a primary data source. Established approaches should be considered limited, however, because posterior estimation either requires prespecification of a shrinkage weight for each source or relies on the data to inform a single parameter, which determines the extent of influence or shrinkage from all sources, risking considerable bias or minimal borrowing. We introduce multisource exchangeability models (MEMs), a general Bayesian approach for integrating multiple, potentially non-exchangeable, supplemental data sources into the analysis of a primary data source. Our proposed modeling framework yields source-specific smoothing parameters that can be estimated in the presence of the data to facilitate a dynamic multi-resolution smoothed estimator that is asymptotically consistent while reducing the dimensionality of the prior space. When compared with competing Bayesian hierarchical modeling strategies, we demonstrate that MEMs achieve approximately 2.2 times larger median effective supplemental sample size when the supplemental data sources are exchangeable as well as a 56% reduction in bias when there is heterogeneity among the supplemental sources. We illustrate the application of MEMs using a recently completed randomized trial of very low nicotine content cigarettes, which resulted in a 30% improvement in efficiency compared with the standard analysis. [ABSTRACT FROM AUTHOR]

Full-waveforminversion (FWI) is not yet a mature imaging technology for lithospheric imaging from teleseismic data. Therefore, its promise and pitfalls need to be assessed more accurately according to the specifications of teleseismic experiments. Three important issues are related to (1) the choice of the lithospheric parametrization for optimization and visualization, (2) the initial model and (3) the acquisition design, in particular in terms of receiver spread and sampling. These three issues are investigated with a realistic synthetic example inspired by the CIFALPS experiment in the Western Alps. Isotropic elastic FWI is implemented with an adjoint-state formalism and aims to update three parameter classes byminimization of a classical least-squares difference-based misfit function. Three different subsurface parametrizations, combining density (ρ) with P and S wave speeds (Vp and Vs), P and S impedances (Ip and Is), or elastic moduli (λ and μ) are first discussed based on their radiation patterns before their assessment by FWI. We conclude that the (ρ, λ, μ) parametrization provides the FWI models that best correlate with the true ones after recombining a posteriori the (ρ, λ, μ) optimization parameters into Ip and Is. Owing to the lowfrequency content of teleseismic data, 1-D reference global models as PREM provide sufficiently accurate initial models for FWI after smoothing that is necessary to remove the imprint of the layering. Two kinds of station deployments are assessed: coarse areal geometry versus dense linear one. We unambiguously conclude that a coarse areal geometry should be favoured as it dramatically increases the penetration in depth of the imaging as well as the horizontal resolution. This results because the areal geometry significantly increases local wavenumber coverage, through a broader sampling of the scattering and dip angles, compared to a linear deployment. [ABSTRACT FROM AUTHOR]

We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain. [ABSTRACT FROM AUTHOR]

We consider the optimization of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall (1991). In particular: (i) we generalize the original method to the case of penalties that are linear in several smoothing parameters, thereby covering the important cases of tensor product and adaptive smoothers; (ii) we show why the method's steps increase the restricted marginal likelihood of the model, that it tends to converge faster than the EM algorithm, or obvious accelerations of this, and investigate its relation to Newton optimization; (iii) we generalize the method to any Fisher regular likelihood. The method represents a considerable simplification over existing methods of estimating smoothing parameters in the context of regular likelihoods, without sacrificing generality: for example, it is only necessary to compute with the same first and second derivatives of the log-likelihood required for coefficient estimation, and not with the third or fourth order derivatives required by alternative approaches. Examples are provided which would have been impossible or impractical with pre-existing Fellner-Schall methods, along with an example of a Tweedie location, scale and shape model which would be a challenge for alternative methods, and a sparse additive modeling example where the method facilitates computational efficiency gains of several orders of magnitude. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. [ABSTRACT FROM AUTHOR]

The problem of modeling the dynamical regulation process within a gene network has been of great interest for a long time. We propose to model this dynamical system with a large number of nonlinear ordinary differential equations (ODEs), in which the regulation function is estimated directly from data without any parametric assumption. Most current research assumes the gene regulation network is static, but in reality, the connection and regulation function of the network may change with time or environment. This change is reflected in our dynamical model by allowing the regulation function varying with the gene expression and forcing this regulation function to be zero if no regulation happens. We introduce a statistical method called functional SCAD to estimate a time-varying sparse and directed gene regulation network, and simultaneously, to provide a smooth estimation of the regulation function and identify the interval in which no regulation effect exists. The finite sample performance of the proposed method is investigated in a Monte Carlo simulation study. Our method is demonstrated by estimating a time-varying directed gene regulation network of 20 genes involved in muscle development during the embryonic stage of Drosophila melanogaster. [ABSTRACT FROM AUTHOR]

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. [ABSTRACT FROM AUTHOR]

Synthetic fault-zone trapped wave (FZTW) dispersion curves and amplitude responses for FL (Love) and FR (Rayleigh) type phases are analysed in transversely isotropic 1-D elastic models. We explore the effects of velocity gradients, anisotropy, source location and mechanism. These experiments suggest: (i) A smooth exponentially decaying velocity model produces a significantly different dispersion curve to that of a three-layer model, with the main difference being that Airy phases are not produced. (ii) The FZTW dispersion and amplitude information of a waveguide with transverse-isotropy depends mostly on the Shear wave velocities in the direction parallel with the fault, particularly if the fault zone to country-rock velocity contrast is small. In this low velocity contrast situation, fully isotropic approximations to a transversely isotropic velocity model can be made. (iii) Fault-aligned fractures and/or bedding in the fault zone that cause transverse-isotropy enhance the amplitude and wave-train length of the FR type FZTW. (iv) Moving the source and/or receiver away from the fault zone removes the higher frequencies first, similar to attenuation. (v) In most physically realistic cases, the radial component of the FR type FZTW is significantly smaller in amplitude than the transverse. [ABSTRACT FROM AUTHOR]

The reconstruction algorithm introduced by Eisenstein et al., which iswidely used in clustering analysis, is based on the inference of the first-order Lagrangian displacement field from the Gaussian smoothed galaxy density field in redshift space. The smoothing scale applied to the density field affects the inferred displacement field that is used to move the galaxies and partially erases the non-linear evolution of the density field. In this article, we explore this crucial step in the reconstruction algorithm. We study the performance of the reconstruction technique using two metrics: first, we study the performance using the anisotropic clustering, extending previous studies focused on isotropic clustering; secondly, we study its effect on the displacement field. We find that smoothing has a strong effect in the quadrupole of the correlation function and affects the accuracy and precision with which we can measure DA(z) and H(z). We find that the optimal smoothing scale to use in the reconstruction algorithm applied to Baryonic Oscillations Spectroscopic Survey-Constant (stellar) MASS (CMASS) is between 5 and 10 h-1 Mpc. Varying from the 'usual' 15-5 h-1 Mpc shows ∼0.3 per cent variations in DA(z) and ∼0.4 per cent H(z) and uncertainties are also reduced by 40 per cent and 30 per cent, respectively. We also find that the accuracy of velocity field reconstruction depends strongly on the smoothing scale used for the density field. We measure the bias and uncertainties associated with different choices of smoothing length. [ABSTRACT FROM AUTHOR]

We study the representability of motivic spheres by smooth varieties. We show that certain explicit "split" quadric hypersurfaces have the A¹-homotopy type of motivic spheres over the integers and that the A¹-homotopy types of other motivic spheres do not contain smooth schemes as representatives. We then study some applications of these representability/non-representability results to the construction of new exotic A¹-contractible smooth schemes. Then, we study vector bundles on even dimensional "split" quadric hypersurfaces by developing an algebro-geometric variant of the classical construction of vector bundles on spheres via clutching functions. [ABSTRACT FROM AUTHOR]

Case-cohort (Prentice, 1986) and nested case-control (Thomas, 1977) designs have been widely used as a cost-effective alternative to the full-cohort design. In this article, we propose an efficient likelihood-based estimation method for the accelerated failure time model under case-cohort and nested case-control designs. An EM algorithm is developed to maximize the likelihood function and a kernel smoothing technique is adopted to facilitate the estimation in the M-step of the EM algorithm. We show that the proposed estimators for the regression coefficients are consistent and asymptotically normal. The asymptotic variance of the estimators can be consistently estimated using an EM-aided numerical differentiation method. Simulation studies are conducted to evaluate the finite-sample performance of the estimators and an application to a Wilms tumor data set is also given to illustrate the methodology. [ABSTRACT FROM AUTHOR]

In this paper, in-sample forecasting is defined as forecasting a structured density to sets where it is unobserved. The structured density consists of one-dimensional in-sample components that identify the density on such sets. We focus on the multiplicative density structure, which has recently been seen as the underlying structure of non-life insurance forecasts. In non-life insurance, the in-sample area is defined as one triangle and the forecasting area as the triangle which, added to the first triangle, completes a square. In recent approaches, two one-dimensional components are estimated by projecting an unstructured two-dimensional density estimator onto the space of multiplicatively separable functions. We show that time-reversal reduces the problem to two one-dimensional problems, where the one-dimensional data are left-truncated and a onedimensional survival density estimator is needed. We then use the local linear density smoother with weighted crossvalidated and do-validated bandwidth selectors. Full asymptotic theory is provided, with and without time-reversal. Finite-sample studies and an application to non-life insurance are included. [ABSTRACT FROM AUTHOR]

We consider curve extension and linear prediction for functional data observed only on a part of their domain, in the form of fragments. We suggest an approach based on a combination of Markov chains and nonparametric smoothing techniques, which enables us to extend the observed fragments and construct approximated prediction intervals around them, construct mean and covariance function estimators, and derive a linear predictor. The procedure is illustrated on real and simulated data. [ABSTRACT FROM AUTHOR]

Body weight (BW) is a critical component for monitoring animal weight gain, body condition, nutritional status. Remote animal weighing systems facilitate frequent collection of animal BW, however, datasets often contain spurious data. The objective of this study was to describe the utility of using a remote Walk-over-Weigh system and subsequent methods for data cleaning. Beef steers (n = 10) were tagged with Electronic RFID tags (EID) in an improved pasture (~12.1 hectares) containing Bermuda and Tall Fescue and inter-seeded with Annual Ryegrass and grazed from Feb. - Dec. 2020. Static chute weights (n = 80) were collected monthly, and a WOW system placed by the water to remotely collect BW (n = 5,466). Data were first loaded into Program R and scanned for spurious data using each of 2 primary approaches, 1) the whole herd and individual means ± 1 standard deviation (SD) calculated daily or over the entire trial and 2) each of 3 data smoothing algorithms, which included a quadratic growth model, cubic splines, and polynomial regression. Then, data with spurious observations removed were paired with static chute weights and fitted to a linear model to measure accuracy (mean bias) and precision (R2) of WOW data. Whole herd mean ± 1SD and individual daily mean ± 1SD identified 1,204 and 1,516 spurious data, with mean bias of -12.46 and -15.37 KG and R2 of 0.90 and 0.68, respectively. Smoothing functions identified 1,707, 4,684, and 4,776 spurious points, with a mean bias of 13.61, -19.78, and 12.58 KG, and R2 of 0.94, 0.70, and 0.87 for quadratic growth models, cubic splines, and polynomial regression, respectively. These results indicate the utility of using a simple WOW system to collect data for measuring growth curves and using weight data in a real-time fashion to make management and marketing decisions. [ABSTRACT FROM AUTHOR]

This article considers the numerical inversion of the power series p(x)=1 + b1x + b²x² +· · · to compute the inverse series q(x) satisfying p(x)q(x)= 1. Numerical inversion is a special case of triangular back-substitution, which has been known for its beguiling numerical stability since the classic work of Wilkinson (1961, Error analysis of direct methods of matrix inversion. J. Assoc. Comput. Mach., 8, 281-330). We prove the numerical stability of inversion of power series and obtain bounds on numerical error. A range of examples show that these bounds overestimate the error by only a few digits. When p(x) is a polynomial and x = a is a root with p(a) = 0, we show that root deflation via the simple division p(x)/(x - a) can trigger instabilities relevant to polynomial root finding and computation of finite-difference weights. When p(x) is a polynomial, the accuracy of the computed inverse q(x) is connected to the pseudozeros of p(x). [ABSTRACT FROM AUTHOR]

In this paper, a modified Chan-Vese model is proposed which is suitable for texture segmentation. The framework is based on a tensor-processed linear structure tensor (LST) as the input to the variational model. A LST is a function of the image gradient which highlights the dominant gradient direction over a neighborhood, while providing a degree of coherence. In the proposed model, the original image is considered as an additional information channel in computing the structure tensor. This nullifies the dislocation of edges to some extent, which otherwise occurs when the structure tensor is processed by the Gaussian smoothing operator. It also enhances the vector magnitude to an appropriate order without losing the directional property due to dislocation. Additionally, an integrated stopping condition is proposed which enables the algorithm to decide the number of iterations adaptively and thus achieve automatic segmentation. The proposed model is applied on suitable test images from the Berkeley Image Database and the results are compared with conventional Chan-Vese, Local Binary Fitting, Gabor-based Chan-Vese and LST integratedmodels. Quantitative and qualitative analyses are presented to illustrate the potential of the proposed model. [ABSTRACT FROM AUTHOR]

An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92, 732–746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley–James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data. [ABSTRACT FROM PUBLISHER]

The log-rank test has been widely used to test treatment effects under the Cox model for censored time-to-event outcomes, though it may lose power substantially when the model's proportional hazards assumption does not hold. In this article, we consider an extended Cox model that uses B-splines or smoothing splines to model a time-varying treatment effect and propose score test statistics for the treatment effect. Our proposed new tests combine statistical evidence from both the magnitude and the shape of the time-varying hazard ratio function, and thus are omnibus and powerful against various types of alternatives. In addition, the new testing framework is applicable to any choice of spline basis functions, including B-splines, and smoothing splines. Simulation studies confirm that the proposed tests performed well in finite samples and were frequently more powerful than conventional tests alone in many settings. The new methods were applied to the HIVNET 012 Study, a randomized clinical trial to assess the efficacy of single-dose Nevirapine against mother-to-child HIV transmission conducted by the HIV Prevention Trial Network. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of various forecasting methods, such as moving average (MA), exponential smoothing (ES) and linear regression (LR) on the bullwhip effect in a four-echelon supply chain. In order to compare the effectiveness of these forecasting methods, a bullwhip effect measure is utilized for two cases: one where the demand is non-trended and one where it has an increasing trend. The forecasting methods in these two cases are ranked based on the size of bullwhip effect they cause, and a statistical method is utilized to ascertain the significance of the differences among these effects. The results obtained show that the LR, double MA and double ES methods result in the least, the second least and the largest bullwhip effect, respectively, in the case of trended demand. Moreover, the simple MA, single ES and LR methods cause the least, the second least and the largest bullwhip effect, respectively, in the case of non-trended demand. Finally, the results are generalized for other tree-like supply chains using an analytical representation. [ABSTRACT FROM AUTHOR]

Summary A dynamic treatment regime consists of a set of decision rules that dictate how to individualize treatment to patients based on available treatment and covariate history. A common method for estimating an optimal dynamic treatment regime from data is Q-learning which involves nonsmooth operations of the data. This nonsmoothness causes standard asymptotic approaches for inference like the bootstrap or Taylor series arguments to breakdown if applied without correction. Here, we consider the m-out-of- n bootstrap for constructing confidence intervals for the parameters indexing the optimal dynamic regime. We propose an adaptive choice of m and show that it produces asymptotically correct confidence sets under fixed alternatives. Furthermore, the proposed method has the advantage of being conceptually and computationally much simple than competing methods possessing this same theoretical property. We provide an extensive simulation study to compare the proposed method with currently available inference procedures. The results suggest that the proposed method delivers nominal coverage while being less conservative than alternatives. The proposed methods are implemented in the qLearn R-package and have been made available on the Comprehensive R-Archive Network (http://cran.r-project.org/). Analysis of the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study is used as an illustrative example. [ABSTRACT FROM AUTHOR]

We study the nonparametric estimation of the cumulative incidence function and the cause-specific hazard function for current status data with competing risks via kernel smoothing. A smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators. Using the smoothed estimators and the plug-in principle, we can estimate the cause-specific hazard function, which has not been studied previously. We also propose semi-smoothed estimators of the cause-specific hazard as an alternative to the smoothed estimator and demonstrate that neither is uniformly more efficient than the other. Numerical studies show that a smoothed bootstrap method works well for selecting the bandwidths in the smoothed nonparametric estimation. The use of the estimators is exemplified by an application to cumulative incidence and hazard of subtype-specific HIV infection from a sero-prevalence study in injecting drug users in Thailand. [ABSTRACT FROM PUBLISHER]

The problem of testing smooth components of an extended generalized additive model for equality to zero is considered. Confidence intervals for such components exhibit good across-the-function coverage probabilities if based on the approximate result , where f is the vector of evaluated values for the smooth component of interest and V f is the covariance matrix for f according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of f=0 is proposed. It is shown that care must be taken in selecting the rank used in the test statistic. The method complements previous work by extending applicability beyond the Gaussian case, while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component’s smoothing penalty. The proposed p-values are routine and efficient to compute from a fitted model, without requiring extra model fits or null distribution simulation. [ABSTRACT FROM PUBLISHER]

One of the key drivers of seasonal behaviour in time series is weather, most notably temperature. Very often weather effects are inter-correlated with the impact of other one-off events like public holidays or promotional activity. Due to the uncertainty that comes with short-term weather forecasts, the exact effect of weather on weekly or daily sales has been given very little attention in the forecasting literature. The present study evaluates the impact of weather-driven adjustments to forecasts in a Brewing company. The forecasting team applies a decomposition approach, where: (a) an exponentially smoothing model is used in order to produce weekly sales forecasts; (b) an econometric model is built once a year in order to estimate the impact of 10-day ahead temperature changes in sales (as an input to this model, weekly weather forecasts from the Met office are used); (c) the sales forecasts from the former are adjusted based on the impacts from the latter, as well as for promotions, one-off events and regular seasonal behaviour. Empirical findings suggest that the weather adjustment mechanism improves the forecasting function in the company. [ABSTRACT FROM PUBLISHER]

The infinite dimension of functional data can challenge conventional methods for classification and clustering. A variety of techniques have been introduced to address this problem, particularly in the case of prediction, but the structural models that they involve can be too inaccurate, or too abstract, or too difficult to interpret, for practitioners. In this paper, we develop approaches to adaptively choose components, enabling classification and clustering to be reduced to finite-dimensional problems. We explore and discuss properties of these methodologies. Our techniques involve methods for estimating classifier error rate and cluster tightness, and for choosing both the number of components, and their locations, to optimize these quantities. A major attraction of this approach is that it allows identification of parts of the function domain that convey important information for classification and clustering. It also permits us to determine regions that are relevant to one of these analyses but not the other. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to investigate a novel nonparametric approach for estimating and smoothing density functions as well as probability densities from discrete samples based on a variational regularization method with the Wasserstein metric as a data fidelity. The approach allows a unified treatment of discrete and continuous probability measures and is hence attractive for various tasks. In particular, the variational model for special regularization functionals yields a natural method for estimating densities and for preserving edges in the case of total variation regularization. In order to compute solutions of the variational problems, a regularized optimal transport problem needs to be solved, for which we discuss several formulations and provide a detailed analysis. Moreover, we compute special self-similar solutions for standard regularization functionals and we discuss several computational approaches and results. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper describes the duchamp source finder, a piece of software designed to find and describe sources in three-dimensional, spectral-line data cubes. duchamp has been developed with H i (neutral hydrogen) observations in mind, but is widely applicable to many types of astronomical images. It features efficient source detection and handling methods, noise suppression via smoothing or multi-resolution wavelet reconstruction, and a range of graphical and text-based outputs to allow the user to understand the detections. This paper details some of the key algorithms used and illustrates the effectiveness of the finder on different data sets. [ABSTRACT FROM AUTHOR]

Motivation: Nuclear magnetic resonance (NMR) has been widely used as a powerful tool to determine the 3D structures of proteins in vivo. However, the post-spectra processing stage of NMR structure determination usually involves a tremendous amount of time and expert knowledge, which includes peak picking, chemical shift assignment and structure calculation steps. Detecting accurate peaks from the NMR spectra is a prerequisite for all following steps, and thus remains a key problem in automatic NMR structure determination.Results: We introduce WaVPeak, a fully automatic peak detection method. WaVPeak first smoothes the given NMR spectrum by wavelets. The peaks are then identified as the local maxima. The false positive peaks are filtered out efficiently by considering the volume of the peaks.WaVPeak has two major advantages over the state-of-the-art peak-picking methods. First, through wavelet-based smoothing, WaVPeak does not eliminate any data point in the spectra. Therefore, WaVPeak is able to detect weak peaks that are embedded in the noise level. NMR spectroscopists need the most help isolating these weak peaks. Second, WaVPeak estimates the volume of the peaks to filter the false positives. This is more reliable than intensity-based filters that are widely used in existing methods.We evaluate the performance of WaVPeak on the benchmark set proposed by PICKY (Alipanahi et al., 2009), one of the most accurate methods in the literature. The dataset comprises 32 2D and 3D spectra from eight different proteins. Experimental results demonstrate that WaVPeak achieves an average of 96%, 91%, 88%, 76% and 85% recall on 15N-HSQC, HNCO, HNCA, HNCACB and CBCA(CO)NH, respectively. When the same number of peaks are considered, WaVPeak significantly outperforms PICKY.Availability: WaVPeak is an open source program. The source code and two test spectra of WaVPeak are available at http://faculty.kaust.edu.sa/sites/xingao/Pages/Publications.aspx. The online server is under construction.Contact: statliuzhi@xmu.edu.cn; ahmed.abbas@kaust.edu.sa; majing@ust.hk; xin.gao@kaust.edu.sa [ABSTRACT FROM AUTHOR]

Summary The accelerated hazard model has been proposed for more than a decade. However, its application is still very limited, partly due to the complexity of the existing semiparametric estimation method. We propose a new semiparametric estimation method based on a kernel-smoothed approximation to the limit of a profile likelihood function of the model. The method leads to smooth estimating equations and is easy to use. The estimates from the method are proved to be consistent and asymptotically normal. Our numerical study shows that the new method is more efficient than the existing method. The proposed method is employed to reanalyze the data from a brain tumor treatment study. [ABSTRACT FROM AUTHOR]

Summary This article presents a new modeling strategy in functional data analysis. We consider the problem of estimating an unknown smooth function given functional data with noise. The unknown function is treated as the realization of a stochastic process, which is incorporated into a diffusion model. The method of smoothing spline estimation is connected to a special case of this approach. The resulting models offer great flexibility to capture the dynamic features of functional data, and allow straightforward and meaningful interpretation. The likelihood of the models is derived with Euler approximation and data augmentation. A unified Bayesian inference method is carried out via a Markov chain Monte Carlo algorithm including a simulation smoother. The proposed models and methods are illustrated on some prostate-specific antigen data, where we also show how the models can be used for forecasting. [ABSTRACT FROM AUTHOR]

Summary Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data. [ABSTRACT FROM AUTHOR]