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Competing procedures, involving data smoothing, weighting, imputation, outlier removal, etc., may be available to prepare data for parametric model estimation. Often, however, little is known about the best choice of preparatory procedure for the planned estimation and the observed data. A machine learning‐based decision rule, an "oracle," can be constructed in such cases to decide the best procedure from a set C$$ \mathcal{C} $$ of available preparatory procedures. The oracle learns the decision regions associated with C$$ \mathcal{C} $$ based on training data synthesized solely from the given data using model parameters with high posterior probability. An estimator in combination with an oracle to guide data preparation is called an oracle estimator. Oracle estimator performance is studied in two estimation problems: slope estimation in simple linear regression (SLR) and changepoint estimation in continuous two‐linear‐segments regression (CTLSR). In both examples, the regression response is given to be increasing, and the oracle must decide whether to isotonically smooth the response data preparatory to fitting the regression model. A measure of performance called headroom is proposed to assess the oracle's potential for reducing estimation error. Experiments with SLR and CTLSR find for important ranges of problem configurations that the headroom is high, the oracle's empirical performance is near the headroom, and the oracle estimator offers clear benefit. [ABSTRACT FROM AUTHOR]

The existing nonuniformity correction methods generally have the defects of image blur, artifacts, image over-smoothing, and nonuniform residuals. It is difficult for these methods to meet the requirements of image enhancement in various complex application scenarios. In particular, when these methods are applied to dim small target images, they may remove dim small targets as noise points due to the image over-smoothing. This paper draws on the idea of a residual network and proposes a two-stage learning network based on the imaging mechanism of an infrared line-scan system. We adopt a multi-scale feature extraction unit and design a gain correction sub-network and an offset correction sub-network, respectively. Then, we pre-train the two sub-networks independently. Finally, we cascade the two sub-networks into a two-stage network and train it. The experimental results show that the PSNR gain of our method can reach more than 15 dB, and it can achieve excellent performance in different backgrounds and different intensities of nonuniform noise. Moreover, our method can avoid losing texture details or dim small targets after effectively removing nonuniform noise. [ABSTRACT FROM AUTHOR]

The performance of ensemble‐based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are not usually known and have to be inferred. Many approaches have been proposed to tackle this problem, including fully Bayesian, likelihood maximization and innovation‐based techniques. This work focuses on maximization of the likelihood function via the expectation–maximization (EM) algorithm to infer the model error covariance combined with ensemble Kalman filters and particle filters to estimate the state. The classical application of the EM algorithm in a data assimilation context involves filtering and smoothing a fixed batch of observations in order to complete a single iteration. This is an inconvenience when using sequential filtering in high‐dimensional applications. Motivated by this, an adaptation of the algorithm that can process observations and update the parameters on the fly, with some underlying simplifications, is presented. The proposed technique was evaluated and achieved good performance in experiments with the Lorenz‐63 and Lorenz‐96 dynamical systems designed to represent some common scenarios in data assimilation such as nonlinearity, chaoticity and model mis‐specification. [ABSTRACT FROM AUTHOR]

We consider the estimation of the variance and spatial scale parameters of the covariance function of a one-dimensional Gaussian process with fixed smoothness parameter s. We study the fixed-domain asymptotic properties of composite likelihood estimators. As an improvement of previous references, we allow for any fixed number of neighbor observation points, both on the left and on the right sides, for the composite likelihood. First, we examine the case where only the variance parameter is unknown. We prove that for small values of s , the composite likelihood estimator converges at a sub-optimal rate and we provide its non-Gaussian asymptotic distribution. For large values of s , the estimator converges at the optimal rate. Second, we consider the case where the variance and the spatial scale are jointly estimated. We obtain the same conclusion as for the first case for the estimation of the microergodic parameter. The theoretical results are confirmed in numerical simulations. • We consider covariance parameter estimation for Gaussian processes. • We study the fixed-domain asymptotic properties of composite likelihood estimators with arbitrary number of neighbor points. • We estimate the variance parameter or the microergodic parameter based on the variance and the spatial scale. • For small values of s of the covariance function, the composite likelihood estimator converges at a sub-optimal rate and its non-Gaussian asymptotic distribution is provided. • For large values of s , the estimator converges at the optimal rate. [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]

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including online and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods. for this article are available online. [ABSTRACT FROM AUTHOR]

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging. [ABSTRACT FROM AUTHOR]

Geoacoustic parameter estimation is presented as a non-linear regression problem where prediction is performed using generalized additive models applied to features extracted from broadband acoustic time-series in a machine learning framework. Qualitatively, it can be seen that signals that have propagated in different environments have distinct structures: in some cases, a single mode is identified, in others, multiple modes can be seen; signals can also be distinguished by different energy levels. Features that are employed here comprise relative amplitudes of distinct peaks in the signals, signal kurtosis, signal strength, decay of the time-series with time, and time difference between distinct peaks of the received signals. Functions are sought that relate sediment sound speed and attenuation to these features. A multivariate generalized additive model is proposed using smoothing splines for the nonlinear regression problem of predicting geoacoustic properties using the features. The spline functions are estimated using noise-free training patterns from known environments. After this training step, the geoacoustic properties are predicted in an efficient manner using noisy testing patterns from a variety of different areas. [ABSTRACT FROM AUTHOR]

We consider the problem of aerodynamic parameter estimation for aircraft dynamics modeled by a state space model where the statistic information of both the process and measurement noises are missing. To deal with the missing statistics, we propose in this work a new approach in which an augmented sigma point Rauch–Tung–Striebel (RTS) Kalman smoother is integrated with the expectation maximization (EM) algorithm. We define a new state vector by combining the original states and the unknown aerodynamic parameters. In addition, we impose a Gaussian random walk model for the unknown aerodynamic parameters and then build the extended state space model for the augmented RTS Kalman smoother. The expectation terms in the EM algorithm are approximated by the sigma point rule which is also applied in the augmented RTS Kalman smoother. Moreover, the non-convex optimization problem involved in the EM is solved in analytical forms rather than in numerical approaches. A comparative study of identifying the aerodynamic parameters of the flight test platform HFB-320 shows that the proposed approach achieves a substantial performance improvement over the existing ones, especially in terms of the convergence rate. [ABSTRACT FROM AUTHOR]

Smoothing techniques are designed to improve the accuracy of equating functions. The main purpose of this study is to compare seven model selection strategies for choosing the smoothing parameter (C) for polynomial loglinear presmoothing and one procedure for model selection in cubic spline postsmoothing for mixed‐format pseudo tests under the random groups design. These model selection strategies were compared for four sample sizes (500, 1,000, 2,000, and 3,000) and two content areas (Advanced Placement [AP] Biology and AP Environmental Science). For polynomial loglinear presmoothing, the Akaike information criterion (AIC) was the only statistic that reduced both random equating error and total equating error in all investigated conditions. Cubic spline postsmoothing tended to produce more accurate results than any of the model selection strategies in polynomial loglinear smoothing. [ABSTRACT FROM AUTHOR]

In this article, we consider a version of the functional Hodrick-Prescott filter for functional time series. We show that the associated optimal smoothing operator preserves the “noise-to-signal ratio” structure. Moreover, as the main result, we propose a consistent estimator of this optimal smoothing operator. [ABSTRACT FROM AUTHOR]

Data smoothing is often required within the environmental data analysis. A number of methods and algorithms that can be applied for data smoothing have been proposed. This paper gives an overview and compares the performance of different smoothing procedures that estimate the trend in the data, based on the surrounding noisy observations that can be applied on environmental data. The considered methods include kernel regression with both global and local bandwidth, moving average, exponential smoothing, robust repeated median regression, trend filtering and approach based on discrete Fourier and discrete wavelet transform. The methods are applied to real data obtained by measurement of PM10 concentrations and compared in a simulation study. [ABSTRACT FROM AUTHOR]

We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifoldsX∘. LetwhereΔgis the Beltrami–Laplace operator on the scattering manifold andVis a real potential function on this setting. We first extend the global-in-time Strichartz estimate in Hassell–Zhang [23] on the requirement ofV(z) = O(⟨z⟩−3) toO(⟨z⟩−2) and secondly generalize the result to the scattering manifold with a mild trapped set as well as Bouclet–Mizutani[4] but with a potential. We also obtain a global-in-time local smoothing estimate on this geometry setting. [ABSTRACT FROM PUBLISHER]

Spatial smoothing is a widely used preprocessing scheme to improve the performance of high-resolution parameter estimation algorithms in case of coherent signals or if only a small number of snapshots is available. In this paper, we present a first-order performance analysis of the spatially smoothed versions of $R$-D Standard ESPRIT and $R$-D Unitary ESPRIT for sources with arbitrary signal constellations as well as $R$-D NC Standard ESPRIT and $R$-D NC Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Moreover, no assumptions on the noise statistics are required apart from a zero mean and finite SO moments. We show that both $R$-D NC ESPRIT-type algorithms with spatial smoothing perform asymptotically identical in the high effective SNR regime. Generally, the performance of spatial smoothing based algorithms depends on the number of subarrays, which is a design parameter that needs to be chosen beforehand. In order to gain more insights into the optimal choice of the number of subarrays, we simplify the derived analytical $R$-D mean square error (MSE) expressions for the special case of a single source. The obtained MSE expression explicitly depends on the number of subarrays in each dimension, which allows us to analytically find the optimal number of subarrays for spatial smoothing. Based on this result, we additionally derive the maximum asymptotic gain from spatial smoothing and compute the asymptotic efficiency for the single source case in closed-form. All the analytical results are verified by simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the non parametric drift estimation for the jump-diffusion model. We employ the double-smoothed non parametric method, and establish the strong consistency and asymptotic normality for estimator. [ABSTRACT FROM AUTHOR]

Different from traditional centralized control, one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems. Currently, most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs. In this paper, we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high-order multi-agent systems subjected to mismatched unknown parameters and uncertain external disturbances. By introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design, a new backstepping based distributed adaptive control protocol is proposed. An extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors’ dynamics, which avoids information exchange of local neighborhood consensus errors among connected subsystems. It is shown that global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme. [ABSTRACT FROM AUTHOR]

The exponentially weighted moving average (EWMA) model has been successfully used in acceptance sampling plans. The EWMA model provides the quality information of the current lot and the preceding lots. In addition, a multiple dependent state (MDS) sampling plan considers the quality information of the preceding lots. In this study, we present two new sampling plans for linear profiles. One is based on EWMA model with yield index using the single sampling plan, and the other is based on EWMA model with yield index using the MDS sampling plans. The plan parameters are determined by a nonlinear optimization approach. As the smoothing parameter value equals to one, the first proposed plan becomes the traditional single sampling plan. In addition, we compare the proposed plans with the traditional single sampling plan. The results indicate that the MDS sampling plan based on EWMA model with yield index with smaller value of smoothing parameter performs better than the traditional single sampling plan and the single sampling plan based on EWMA model with yield index in terms of the sample size required. One real example is used to illustrate the proposed plan. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Generalized cross-validation (GCV) is a popular parameter selection criterion for spline smoothing of noisy data, but it sometimes yields a severely undersmoothed estimate, especially if the sample size is small. Robust GCV (RGCV) and modified GCV are stable extensions of GCV, with the degree of stabilization depending on a parameter $$\gamma \in (0,1)$$ for RGCV and on a parameter $$\rho >1$$ for modified GCV. While there are favorable asymptotic results about the performance of RGCV and modified GCV, little is known for finite samples. In a large simulation study with cubic splines, we investigate the behavior of the optimal values of $$\gamma $$ and $$\rho $$ , and identify simple practical rules to choose them that are close to optimal. With these rules, both RGCV and modified GCV perform significantly better than GCV. The performance is defined in terms of the Sobolev error, which is shown by example to be more consistent with a visual assessment of the fit than the prediction error (average squared error). The results are consistent with known asymptotic results. [ABSTRACT FROM AUTHOR]

A new inference approach to general dynamic models of gene regulatory networks (GRN) is introduced. The methodology is based on a Maximum a Posteriori (MAP) smoothing of time series data from which mean field variables of the dynamics are estimated. The interactions are modeled by a Continuous Time Recurrent Neural Network (CTRNN). Parameter estimation of the CTRNN is performed without the need to numerically solve the system of nonlinear differential equations. The method is tested on a benchmark of real genetic networks and displays superior performance, in terms of the mean squared error of the expression dynamics, compared to other formalisms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new estimation method for randomly right censored varying coefficient models and establish the asymptotic normality of the resulting estimator. Compared to the existing estimation method, the proposed estimation method is computationally simple and practically feasible since it requires no transformation of data. Simulation studies are conducted to assess the finite sample performance of the proposed estimation method against that of the existing estimation method. The simulation results demonstrate that the proposed estimation method performs much better than the existing estimation method. [ABSTRACT FROM AUTHOR]

Reanalysis data sets have become a popular data source for large-scale wind power analyses because they cover large areas and long time spans, but those data are uncertain representations of “true” wind speeds. In this work we develop a model that systematically quantifies the uncertainties across many sites and corrects for biases of the reanalysis data. We apply this model to 32 years of reanalysis data for 1002 plausible wind-plant sites in the U.S. Great Plains to estimate variability of wind energy generation and the smoothing effect of aggregating distant wind plants. We find the coefficient of variation (COV) of annual energy generation of individual wind plants in the Great Plains is 5–12%, but the COV of all those plants aggregated together is 3.0%. The year-to-year variability (of interest to system planners) shows a maximum step change of ∼10%, and the wind power varies by ±7.5% over a 32-year period. Similarly, the average variability of quarterly cash flow to equity investors in a single wind plant is 29%, but that can be reduced to 18–21% by creating small portfolios of two wind plants selected from regions with low correlations of wind speed. [ABSTRACT FROM AUTHOR]

We develop a generalized additive modeling framework for taking into account the effect of predictors on the dependence structure between two variables. We consider dependence or concordance measures that are solely functions of the copula, because they contain no marginal information: rank correlation coefficients or tail-dependence coefficients represent natural choices. We propose a maximum penalized log-likelihood estimator, derive its n -consistency and asymptotic normality, discuss details of the estimation procedure and the selection of the smoothing parameter. Finally, we present the results from a simulation study and apply the new methodology to a real dataset. Using intraday asset returns, we show that an intraday dependence pattern, due to the cyclical nature of market activity, is shaped similarly to the individual conditional second moments. [ABSTRACT FROM AUTHOR]

The problem of bandwidth selection for kernel-based estimation of the distribution function (cdf) at a given point is considered. With appropriate bandwidth, a kernel-based estimator (kdf) is known to outperform the empirical distribution function. However, such a bandwidth is unknown in practice. In pointwise estimation, the appropriate bandwidth depends on the point where the function is estimated. The existing smoothing methods use one common bandwidth to estimate the cdf. The accuracy of the resulting estimates varies substantially depending on the cdf and the point where it is estimated. We propose to select bandwidth by minimizing a bootstrap estimator of the MSE of the kdf. The resulting estimator performs reliably, irrespective of where the cdf is estimated. It is shown to be consistent under i.i.d. as well as strongly mixing dependence assumption. Two applications of the proposed estimator are shown in finance and seismology. We report a dataset on the S & P Nifty index values. [ABSTRACT FROM AUTHOR]

In this paper, ridge and non-ridge type shrinkage estimators and their positive parts are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. Also, necessary and sufficient conditions, for the superiority of the ridge type estimator over its counterpart, for selecting the ridge parameter k are obtained. Lastly, a simulation study and real data analysis are performed to illustrate the efficiency of proposed estimators based on the minimum risk criterion. In this regard, kernel smoothing and modified cross-validation methods for estimating the non-parametric function are used. [ABSTRACT FROM AUTHOR]

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and sparse estimation simultaneously. We establish the convergence rate and oracle properties of the estimator under weak regularity conditions. Remarkably, the estimated parametric components are sparse and efficient, and the nonparametric component can be estimated with the optimal rate. The procedure also has attractive computational properties. Using the representer theory of smoothing splines, we reformulate the objective function as a LASSO-type problem, enabling us to use the LARS algorithm to compute the solution path. We then extend the procedure to situations when the number of predictors increases with the sample size and investigate its asymptotic properties in that context. Finite-sample performance is illustrated by simulations. [ABSTRACT FROM AUTHOR]

Consider the semiparametric transformation model $$\Lambda _{\theta _o}(Y)=m(X)+\varepsilon $$ , where $$\theta _o$$ is an unknown finite dimensional parameter, the functions $$\Lambda _{\theta _o}$$ and $$m$$ are smooth, $$\varepsilon $$ is independent of $$X$$ , and $${\mathbb {E}}(\varepsilon )=0$$ . We propose a kernel-type estimator of the density of the error $$\varepsilon $$ , and prove its asymptotic normality. The estimated errors, which lie at the basis of this estimator, are obtained from a profile likelihood estimator of $$\theta _o$$ and a nonparametric kernel estimator of $$m$$ . The practical performance of the proposed density estimator is evaluated in a simulation study. [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]

In this paper, we propose a novel approach to limited vocabulary recognition of unconstrained (mixed cursive) handwriting based on a hidden Markov model (HMM). Here, an input word sample is segmented into sub-strokes. However, instead of recognizing individual sub-strokes, we recognize the whole word sample as a basic unit. In this study, we consider both circular and linear features. The von Mises distribution is used to model circular feature components while the Gaussian distribution is used for the linear features. We implement fully connected non-homogeneous HMMs considering the enormous variability in the present handwriting style which often includes delayed strokes. Since such an HMM involves a large number of parameters, we implement a simple but novel approach to smoothing of HMM parameters to avoid possible over-fitting and poor generalization. Finally, in the proposed approach, we combine recognition results of two HMMs: one considering the input sample in the natural order and the other considering the sample in the reverse order. A major goal of the present study is to develop an efficient recognition scheme for online unconstrained handwritten words of Bangla, a popular Indic script. [ABSTRACT FROM AUTHOR]

In a generalized linear model, the mean of the response variable is a possibly non-linear function of a linear combination of explanatory variables. When the nonlinear function is unknown and is estimated nonparametrically from the data, these models are known as single index models. Using the relation of generalized linear models with the exponential family model, this paper shows how to use a modified version of the empirical cumulant generating function to estimate the linear function of the explanatory variables with no need of smoothing techniques. The resulting estimator is consistent and normally distributed. Extensive simulations, partially reported here, show that the method works in practice. The method can also be seen as complementary to existing fully nonparametric methods. In fact, it can provide an initial value that can be used to fine tune a nonparametric estimator of the link function in the first step of the estimation. [ABSTRACT FROM AUTHOR]

The geographical relative risk function is a useful tool for investigating the spatial distribution of disease based on case and control data. The most common way of estimating this function is using the ratio of bivariate kernel density estimates constructed from the locations of cases and controls, respectively. An alternative is to use a local-linear (LL) estimator of the log-relative risk function. In both cases, the choice of bandwidth is critical. In this article, we examine the relative performance of the two estimation techniques using a variety of data-driven bandwidth selection methods, including likelihood cross-validation (CV), least-squares CV, rule-of-thumb reference methods, and a new approximate plug-in (PI) bandwidth for the LL estimator. Our analysis includes the comparison of asymptotic results; a simulation study; and application of the estimators on two real data sets. Our findings suggest that the density ratio method implemented with the least-squares CV bandwidth selector is generally best, with the LL estimator with PI bandwidth being competitive in applications with strong large-scale trends but much worse in situations with elliptical clusters. [ABSTRACT FROM AUTHOR]

Highlights: [•] IAD method for evaluating transfer alignment accuracy is put forward. [•] 4 filtering and smoothing algorithms are analyzed and contrasted. [•] Estimation mathematic model was built. [•] Evaluation scheme of transfer alignment on moving base was designed. [Copyright &y& Elsevier]

Abstract: In this paper we consider partially linear varying coefficient models. We provide semiparametric efficient estimators of the parametric part as well as rate-optimal estimators of the nonparametric part. In our model, different nonparametric coefficients have different smoothing variables. This requires employing a projection technique to get proper estimators of the nonparametric coefficients, and thus conventional kernel smoothing cannot give semiparametric efficient estimators of the parametric components. We take the smooth backfitting approach in conjunction with the profiling technique to get semiparametric efficient estimators of the parametric part. We also show that our estimators of the nonparametric part achieve the univariate rate of convergence, regardless of the covariate’s dimension. We report the finite sample properties of the semiparametric efficient estimators and compare them with those of other estimators. [Copyright &y& Elsevier]

Penalized spline estimator is one of the useful smoothing methods. To construct the estimator, having goodness of fit and smoothness, the smoothing parameter should be appropriately selected. The purpose of this paper is to select the smoothing parameter using the asymptotic property of the penalized splines. The new smoothing parameter selectionmethod is established in the context of minimization asymptotic form of MISE of the penalized splines. The mathematical and the numerical properties of the proposedmethod are studied. First we organize the newmethod in univariate regressionmodel. Next we extend to the additive models. A simulation study to confirm the efficiency of the proposed method is addressed. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of different estimations of the partially linear models based on the smoothing spline technique. Performance of this technique greatly depends on the selection of smoothing parameters. Many methods of selecting smoothing parameters such as an improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows' Cp criterion, risk estimation using classical pilots (REC) and local risk estimation (LRS) are developed in literature. The smoothing parameter selection has been discussed in respect to a smoothing spline implementation in predicting the partially linear model (PLM). To this end, a simulation study has been conducted to evaluate and compare the performance of six selection methods. In this connection, 1000 replications have been performed in simulation for sample sets with different sizes. The AICc method is recommended since it is stable and works well in all simulations. It performs better than other methods especially when the sample sizes are not large. [ABSTRACT FROM AUTHOR]

Highlights: [•] We address the parameterization of exponential smoothing forecasting models. [•] We empirically test derivative-free methods for models’ parameterization. [•] We adapt the exponential smoothing model to handle box-constraints. [•] Derivative-free methods almost equaled the performance of a gradient-based method. [•] Derivative-free methods resulted faster than the gradient-based method. [ABSTRACT FROM AUTHOR]

An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter $$k$$. One way to choose $$k$$ based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is similarly important as the choice of the smoother. Especially, when outliers are present, robust cross-validation criteria are needed. So far little is known about the behaviour of robust cross-validated smoothers in the presence of discontinuities in the regression function. We combine different smoothing procedures based on local constant fits with each of several cross-validation criteria. These combinations are compared in a simulation study under a broad variety of data situations with outliers and abrupt jumps. There is not a single overall best cross-validation criterion, but we find Boente-cross-validation to perform well in case of large percentages of outliers and the Tukey-criterion in case of data situations with jumps, even if the data are contaminated with outliers. [ABSTRACT FROM AUTHOR]

In the present article, we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed. [ABSTRACT FROM AUTHOR]

Abstract: CO2 concentrations recorded for two years using a Picarro G1301 analyser at a rural site were studied applying two procedures. Firstly, the smoothing kernel method, which to date has been used with one linear and another circular variable, was used with pairs of circular variables: wind direction, time of day, and time of year, providing that the daily cycle was the prevailing cyclical evolution and that the highest concentrations were justified by the influence of one nearby city source, which was only revealed by directional analysis. Secondly, histograms were obtained, and these revealed most observations to be located between 380 and 410ppm, and that there was a sharp contrast during the year. Finally, histograms were fitted to 14 distributions, the best known using analytical procedures, and the remainder using numerical procedures. RMSE was used as the goodness of fit indicator to compare and select distributions. Most functions provided similar RMSE values. However, the best fits were obtained using numerical procedures due to their greater flexibility, the triangular distribution being the simplest function of this kind. This distribution allowed us to identify directions and months of noticeable CO2 input (SSE and April-May, respectively) as well as the daily cycle of the distribution symmetry. Among the functions whose parameters were calculated using an analytical expression, Erlang distributions provided satisfactory fits for monthly analysis, and gamma for the rest. By contrast, the Rayleigh and Weibull distributions gave the worst RMSE values. [Copyright &y& Elsevier]

Abstract: In this paper, penalized estimating equations are proposed to estimate the index parametric components, which is of primary interest, in the partially varying-coefficient single-index models (PVCSIMs). Although some procedures have been developed to estimate the index parameter in PVCSIM, the problem of how to conduct variable selection for the index in such models has not been addressed to date. To solve this problem, we propose a class of efficient penalized estimating equations, which combine the smoothly clipped absolute deviation (SCAD) penalty and a stepwise estimation method. The proposed method can simultaneously select significant variables in the index and estimate the nonzero smooth coefficient parameters. Under suitable conditions, we establish the theoretical properties of our penalized estimating procedure, including the oracle properties and the asymptotic normality for the resulting penalized estimation. We evaluate the performance of the proposed method by using Monte Carlo simulations and the application to a real dataset. [Copyright &y& Elsevier]

Short-term traffic prediction plays an important role in intelligent transport systems. This paper presents a novel two-stage prediction structure using the technique of Singular Spectrum Analysis (SSA) as a data smoothing stage to improve the prediction accuracy. Moreover, a novel prediction method named Grey System Model (GM) is introduced to reduce the dependency on method training and parameter optimisation. To demonstrate the effects of these improvements, this paper compares the prediction accuracies of SSA and non-SSA model structures using both a GM and a more conventional Seasonal Auto-Regressive Integrated Moving Average (SARIMA) prediction model. These methods were calibrated and evaluated using traffic flow data from a corridor in Central London under both normal and incident traffic conditions. The prediction accuracy comparisons show that the SSA method as a data smoothing step before the application of machine learning or statistical prediction methods can improve the final traffic prediction accuracy. In addition, the results indicate that the relatively novel GM method outperforms SARIMA under both normal and incident traffic conditions on urban roads. [ABSTRACT FROM PUBLISHER]

We consider the smoothing problem for a general state space system using sequential Monte Carlo (SMC) methods. The marginal smoother is assumed to be available in the form of weighted random particles from the SMC output. New algorithms are developed to extract the smoothed marginal maximum a posteriori (MAP) estimate of the state from the existing marginal particle smoother. Our method does not need any kernel fitting to obtain the posterior density from the particle smoother. The proposed estimator is then successfully applied to find the unknown initial state of a dynamical system and to address the issue of parameter estimation problem in state space models. [ABSTRACT FROM PUBLISHER]