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We describe the intersection of the Torelli locus j(\mathcal {M}_4^{ct}) = \mathcal {J}_4 with Newton and Ekedahl-Oort strata related to the supersingular locus in characteristic 2. We show that the locus of supersingular Jacobians \mathcal {S}_4\cap \mathcal {J}_4 in characteristic 2 is pure of dimension three. One way to obtain that result uses an analysis of the data of smooth genus four curves and principally polarized abelian fourfolds defined over \mathbb {F}_2, and another involves a more careful study of some relevant Ekedahl-Oort loci. [ABSTRACT FROM AUTHOR]

In areas ranging from neuroimaging to climate science, advances in data storage and sensor technology have led to a proliferation in multidimensional functional datasets. A common approach to analyzing functional data is to first map the discretely observed functional samples into continuous representations, and then perform downstream statistical analysis on these smooth representations. It is well known that many of the traditional approaches used for 1D functional data representation are plagued by the curse of dimensionality and quickly become intractable as the dimension of the domain increases. In this article, we propose a computational framework for learning continuous representations from a sample of multidimensional functional data that is immune to several manifestations of the curse. The representations are constructed using a set of separable basis functions that are defined to be optimally adapted to the data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition of a carefully defined reduction transformation of the observed data. Roughness-based regularization is incorporated using a class of differential operator-based penalties. Relevant theoretical properties are also discussed. The advantages of our method over competing methods are thoroughly demonstrated in simulations. We conclude with a real data application of our method to a clinical diffusion MRI dataset. for this article are available online. [ABSTRACT FROM AUTHOR]

Sampling variance smoothing is an important topic in small area estimation. In this article, we propose sampling variance smoothing methods for small area proportion estimation. In particular, we consider the generalized variance function and design effect methods for sampling variance smoothing. We evaluate and compare the smoothed sampling variances and small area estimates based on the smoothed variance estimates through analysis of survey data from Statistics Canada. The results from real data analysis and simulation study indicate that the proposed sampling variance smoothing methods perform very well for small area estimation. [ABSTRACT FROM AUTHOR]

This paper aims to present an overview of Semiparametric additive models. An estimation of the finite‐parameters of semiparametric regression models that involve additive nonparametric components is explained, including their historical background. In addition, three different smoothing techniques are considered in order to show the working procedures of the estimators and to explore their statistical properties: smoothing splines, kernel smoothing and local linear regression. These methods are compared with respect to both their theoretical and practical behaviors. A simulation study and a real data example are carried out to reveal the performances of the three methods. Accordingly, the advantages and disadvantages of each method regarding semiparametric additive models are presented based on their comparative scores using determined evaluation metrics for loss of information. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Modeling MethodsStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical Models > Semiparametric Models [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]

Anomaly detection through data analysis helps to accurately identify abnormal behaviors, improving service quality and decision-making capabilities. However, due to the temporal and spatial dependence of multi-dimensional time series data and the randomness of ab normal events, the existing methods still have certain limitations. Regarding the issue above, this paper proposed a multi-dimensional time series data anomaly detection method MBCLE, which combined new statistical methods and bidirectional convolutional LSTM. The method introduced a stacked median filter to handle point anomalies in the input data and smooth data fluctuations, and designed a neural network predictor combining Bi-ConvLSTM and Bi-LSTM for data modeling and prediction. It smoothed the prediction errors using bidirectional recurrent exponentially weighted moving average ( BrEWMA) . The method used dynamic threshold to calculate the threshold to detect contextual anomalies. The experimental results show that MBCLE has good detection performance and each step contributes to the performance improvement. [ABSTRACT FROM AUTHOR]

We performed two simulation studies that investigated dimensionality recovery in NPD tetrachoric correlation matrices using parallel analysis. In each study, the NPD matrices were rehabilitated by three smoothing algorithms. In Study 1, we replicated the work by Debelak and Tran on the assessment of dimensionality in one- or two-dimensional common factor models. In Study 2, we extended the Debelak and Tran design in three important ways. Specifically, we investigated: (a) a wider range of factors; (b) models with varying amounts of model error; and (c) models generated from more realistic population item parameters. Our results indicated that matrix smoothing of NPD tetrachoric correlation matrices improves the performance of parallel analysis with binary data. However, these improvements were modest and often of trivial size. To demonstrate the effect of matrix smoothing on an empirical data set, we applied parallel analysis and factor analysis to Adjective Checklist data from the California Twin Registry. [ABSTRACT FROM AUTHOR]

We consider the problem of efficiently online computing/filtering or analysis multimedia streams. In this scenario, we register a large scale of continuous analysis queries to filter pornographic stream items. Each query is a conjunction of filters. For instance, the query "does this image contain a people basking in the beach?" can be resolved by applying the conjunction of water, people, sand, sea filters successively on the stream item. However, the online evaluation of multimedia filters is indeed very expensive, fortunately there usually exist multiple filters shared among a lot of queries. In other words, each filter may occur in multiple queries. An open problem in such a filtering scenario is how to order the filters in an optimal sequence to achieve significant performance. Existing methods are based on a greedy strategy which orders the filters according to three factors (selectivity, popularity, cost). Although all these methods achieve good results, there are still some problems that haven't addressed yet. First, the selectivity factor is set empirically, which can not adaptively adjust with multimedia stream. Second, the proportion relationships among the three factors (selectivity, cost, popularity) were not considerably explored. Under these observations,in this paper, we propose a Dynamic-Analytic hierarchy process Framework (DAF) which use a time-based compositional forecasting method, which is based on the idea of exponential smoothing, to deal with the factors' proportion relationships dynamics. Experiments on both synthetic and real lift multimedia streams demonstrate that our proposed framework (DAF) provides much great adaptability in modeling the factors proportion relationships changing over multimedia stream environment. [ABSTRACT FROM AUTHOR]

Dynamic visualization of multidimensional hydrometeorological data is vital for decision-makers to catch situational awareness and command an emergency response in natural disasters. Nevertheless, few software tools can comprehensively visualize hydrometeorological data in different scales, dimensions, and time. In this paper, an interactive 4D spatio-temporal visualization system based on a virtual globe is proposed. Voxel-based data model and multi-level index are adopted to organize the field data in a unified data structure. Meanwhile, it is resampled in both spatial and temporal dimensions in memory to prepare smooth data stream for rendering. Ten field models, including large-scale volume rendering and adaptive streamline rendering, are accelerated and integrated to display the field data collaboratively. The profile analysis and eddy tracking improve user experience in interactively exploring specific scenes. The system is tested against both large-scale meteorological data in the atmosphere and small-scale hydrological data at the surface, using typhoon landfall and riverine flood, respectively. The results demonstrate the applicability and efficiency of the system to dynamically visualize hydrometeorological data. [ABSTRACT FROM AUTHOR]

In the liquefied petroleum gas (LPG) cylinder business, one of the most important assets is the LPG cylinder. This work addresses the asset acquisition planning for the LPG cylinder business of a company from the energy sector which has recently started this activity. In order to make the acquisition plan, it was necessary to forecast the sales and the LPG cylinder return rate. For that purpose, an ensemble method using time series techniques, multiple linear regression models and artificial neural networks was employed. Sales forecast was obtained using time series techniques, in particular, moving averages and exponential smoothing. Then, forecast of bottled propane gas sales and return rate was also addressed through multiple linear regression and artificial neural networks. A probability density function was defined for each of the different approaches. Afterward, using Monte Carlo simulation, the forecast values are obtained by a linear combination of the probability density functions, thus producing the final forecast. Results show that the company's expectation of growth is larger than that predicted by the proposed methodology, which means the company should reflect on its current asset acquisition strategy. By combining different approaches, the proposed multi-model methodology allowed to obtain an accurate forecasting, without requiring a lot of historical data. [ABSTRACT FROM AUTHOR]

The development of sensor technologies and smart devices has made it possible to realize real-time data acquisition of human beings. Human behavior monitoring is the process of obtaining activity information with wearables and computer technology. In this paper, we design a data preprocessing method based on the data collected by a single three-axis accelerometer. We first use Butterworth filter as low-pass filtering to remove the noise. Then, we propose a KGA algorithm to remove abnormal data and smooth them at the same time. This method uses genetic algorithm to optimize the parameters of Kalman filter. After that, we use a threshold-based method to identify falls that are harmful to the elderly. The key point of this method is to distinguish falls from people's daily activities. According to the characteristics of human falls, we extract eigenvalues that can effectively distinguish daily activities from falls. In addition, we use cross-validation to determine the threshold of the method. The results show that in the analysis of 11 kinds of human daily activities and 15 types of falls, our method can distinguish 15 types of falls. The recognition recall rate in our method reaches 99.1%. [ABSTRACT FROM AUTHOR]

Background: High-throughput sequencing experiments followed by differential expression analysis is a widely used approach for detecting genomic biomarkers. A fundamental step in differential expression analysis is to model the association between gene counts and covariates of interest. Existing models assume linear effect of covariates, which is restrictive and may not be sufficient for certain phenotypes. Results: We introduce NBAMSeq, a flexible statistical model based on the generalized additive model and allows for information sharing across genes in variance estimation. Specifically, we model the logarithm of mean gene counts as sums of smooth functions with the smoothing parameters and coefficients estimated simultaneously within a nested iterative method. The variance is estimated by the Bayesian shrinkage approach to fully exploit the information across all genes. Conclusions: Based on extensive simulations and case studies of RNA-Seq data, we show that NBAMSeq offers improved performance in detecting nonlinear effect and maintains equivalent performance in detecting linear effect compared to existing methods. The vignette and source code of NBAMSeq are available at http://bioconductor.org/packages/release/bioc/html/NBAMSeq.html. [ABSTRACT FROM AUTHOR]

Derivatives play an important role in bandwidth selection methods (e.g., plug-ins), data analysis and bias-corrected confidence intervals. Therefore, obtaining accurate derivative information is crucial. Although many derivative estimation methods exist, the majority require a fixed design assumption. In this paper, we propose an effective and fully data-driven framework to estimate the first and second order derivative in random design. We establish the asymptotic properties of the proposed derivative estimator, and also propose a fast selection method for the tuning parameters. The performance and flexibility of the method is illustrated via an extensive simulation study. [ABSTRACT FROM AUTHOR]

In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we propose a new method of local search to estimate the structural dimensions. Simulations and real data analysis support the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the quantile varying coefficient model for longitudinal data, where the unknown nonparametric functions are approximated by polynomial splines and the estimators are obtained by minimizing the quadratic inference function. The theoretical properties of the resulting estimators are established, and they achieve the optimal convergence rate for the nonparametric functions. Since the objective function is non-smooth, an estimation procedure is proposed that uses induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. Moreover, we propose a variable selection procedure based on the regularization method, which can simultaneously estimate and select important nonparametric components and has the asymptotic oracle property. Extensive simulations and a real data analysis show the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Functional data analysis has attracted substantial research interest and the goal of functional sparsity is to produce a sparse estimate which assigns zero values over regions where the true underlying function is zero, i.e. no relationship between the response variable and the predictor variable. In this paper, we consider a functional linear regression model that explicitly incorporates the interconnections among the responses. We propose a locally sparse (i.e. zero on some subregions) estimator, multiple-smooth and locally sparse (m-SLoS) estimator, for coefficient functions base on the interconnections among the responses. Simulations show excellent numerical performance of the proposed method in terms of the estimation of coefficient functions especially the coefficient functions are same for all multivariate responses. Practical merit of this modelling is demonstrated by one real application and the prediction shows significant improvements. [ABSTRACT FROM AUTHOR]

The efficient estimation of regression coefficients in the longitudinal data analysis requires a correct specification of the covariance structure. Existing approaches usually focus on modeling the mean with specification of certain covariance structures, which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs. In this article, we propose a novel data-driven approach based on semiparametric varying-coefficient models to model the mean and the covariance simultaneously, motivated by the modified Cholesky decomposition. An iterative estimation method is proposed, consisting of an orthogonality-based technique for parameters, an adaptive jump-preserving estimation method for varying coefficients, a modification of local linear smoothing technique for the autoregressive coefficient function, and a kernel smoothing technique for the variance function. Theoretical properties of the resulting estimators including uniform consistency and asymptotic normality are explicitly studied under certain mild conditions. Simulation studies are carried out to evaluate the efficacy of the proposed methods, and an analysis of a real data example is provided for illustration. [ABSTRACT FROM AUTHOR]

Many experiments aim to investigate the time-course of cognitive processes while measuring a single response per trial. A common first step in the analysis of such data is to divide them into a limited number of bins. As we demonstrate here, the way one chooses these bins can considerably influence the resulting time-course. As a solution to this problem, we here present the smoothing method for analysis of response time-course (SMART)—a complete package for reconstructing the time-course from one-sample-per-trial data and performing statistical analysis. After smoothing the data, the SMART weights the data based on the effective number of data points per participant. A cluster-based permutation test then determines at which moments the responses differ from a baseline or between two conditions. We show here that, in contrast to contemporary binning methods, the chosen temporal resolution has a negligible effect on the SMART reconstructed time-course. To facilitate its use, the SMART method, accompanied by a tutorial, is available as an open-source package. [ABSTRACT FROM AUTHOR]

We propose a combination of portable X-ray fluorescence (pXRF) and chemometrics to discriminate between Mesoamerican obsidian sources and to assign archaeological artifacts of unknown origin to their respective deposits using a procedure that does not require any type of calibration or reference standards. A set of 109 samples of known origin and a total of 257 samples of unknown origin were analyzed with a portable XRF spectrometer. The resultant spectra were used as spectral signatures for the chemometric data analysis. First, we applied spectral pre-treatment techniques, such as CluPA algorithm for peak alignment and the Savitzky-Golay and Extended Multiplicative Signal Correction for data smoothing and noise removal, combined with methods for the selection of a spectral range containing the variables with the most relevant information (iPLS and). The full spectrum of the obsidian samples was divided into 20 subintervals, fitting a local regression model (PLS) to each subinterval. The performance was evaluated by the Root Mean Square Error of Cross-Validation, the Root Mean Square Error of Prediction and the correlation coefficient. The selected spectral regions were then analyzed with ROBPCA algorithm for the discrimination of outliers and the projection of the observations in the PCA space. For the classification, we propose a robust procedure (RSIMCA) which is based on a ROBPCA method for high-dimensional data. The classification rules were obtained by using the orthogonal and the score distances, from which it is possible to distinguish samples that belong to a given group. Using the proposed methodology, we were able to provide evidence about which variables were meaningful for the classification and provided information about group membership or provenance. This approach proves to be a valid technique for the quantitative analysis of XRF spectra. [ABSTRACT FROM AUTHOR]

Objective: This paper consists on examining a longitudinal data, output of generated data, via constructing a semiparametric model, the wavelets analysis will be applied as smoothing approach for the nonparametric part of the model. Material and Methods: Mixed effects models have been largely examined due to their flexibility in handling data without constraints. Mixed models could be characterized with their parametric and nonparametric features. Indeed, semiparametric mixed models which combine parametric and nonparametric features, started to receive more attention notably for examining longitudinal data. Regarding the nonparametric features, smoothing approaches should be applied. Recently, the wavelets analysis has been considered as a powerful mathematic tool to decompose a series due to its multiresolution features (frequential and temporal) and some researchers mentioned it as a smoothing approach for large data, but the wavelets features for smoothing still not commonly applied on longitudinal data. Results: A data is generated referring to a previous published hypertension study by National Institute Health. The results show that the wavelets analysis has a strong capacity as smoothing approach compared to well-known other smoothing methods; Root Mean Square Errors are calculated, and via the constructed semiparametric model, it has been confirmed that the incident hypertension is related to the high Systolic blood pressure, high diastolic blood pressure and low BMI. [ABSTRACT FROM AUTHOR]

Point cloud data arises naturally from 3-dimensional scanners, LiDAR sensors, and industrial computed tomography (i.e. CT scans) among other sources. Most point clouds obtained through experimental means exhibit some level of noise, inhibiting mesh reconstruction algorithms and topological data analysis techniques. To alleviate the problems caused by noise, smoothing algorithms are often employed as a preprocessing step. Moving least squares is one such technique, however, many of these techniques are designed to work on surfaces in R3. As interesting point clouds can naturally live in higher dimensions, we seek a method for smoothing higher dimensional point clouds. To this end, we turn to the distance to measure function. In this paper, we provide a theoretical foundation for studying the gradient flow induced by the squared distance to measure function, as introduced by Chazal, Cohen-Steiner, and Mérigot. In particular, we frame the gradient flow as a Filippov system and find a method for solving the squared distance to measure gradient flow, induced by the uniform empirical measure, using higher order Voronoi diagrams. In contrast to some existing techniques, this gradient flow provides a smoothing algorithm which computationally scales with dimensionality. [ABSTRACT FROM AUTHOR]

We consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi-likelihood coupling a modification of the local kernel smoothing method. The proposed estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient in terms of their linear functionals. Their superiority to the competitors is further illustrated numerically through simulation studies. The method is applied to analyze AIDS study and atmospheric study. Supplementary materials for this article are available online. [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]

The evaluation models for long time historical data is important in many applications. In this study, based on Age measure defined by Yager, we propose the definitions of Age Sequence and Age Series. Then, we provide a Generalized Recursive Smoothing method. Some classical smoothing models in evaluation problems can be seen as special cases of Generalized Recursive Smoothing method. In order to obtain more reasonable and effective aggregation results of the historical data, we propose some different Age Sequences, e.g., the Generalized Harmonic Age Sequence and p Age Sequence, which theoretically can provide infinite more recursive smoothing methods satisfying different preferences of decision makers. [ABSTRACT FROM AUTHOR]

In this paper, a novel freeway traffic speed estimation method based on probe data is presented. In contrast to other traffic speed estimators, it only requires velocity data from probes and does not depend on any additional data inputs such as density or flow information. In the first step the method determines the three traffic phases free flow, synchronized flow, and Wide Moving Jam (WMJ) described by Kerner et al. in space and time. Subsequently, reported data is processed with respect to the prevailing traffic phase in order to estimate traffic velocities. This two-step approach allows incorporating empirical features of phase fronts into the estimation procedure. For instance, downstream fronts of WMJs always propagate upstream with approximately constant velocity, and downstream fronts of synchronized flow phases usually stick to bottlenecks. The second step assures the validity of measured velocities is limited to the extent of its assigned phase. Effectively, velocity information in space-time can be estimated more distinctively and the result is therefore more accurate even if the input data density is low. The accuracy of the proposed Phase-Based Smoothing Method (PSM) is evaluated using real floating car data collected during two traffic congestions on the German freeway A99 and compared to the performance of the Generalized Adaptive Smoothing Method (GASM) as well as a naive algorithm. The quantitative and qualitative results show that the PSM reconstructs the congestion pattern more accurately than the other two. A subsequent analysis of the computational efficiency and sensitivity demonstrates its practical suitability. [ABSTRACT FROM AUTHOR]

Root zone soil moisture (RZSM) is an important state variable for understanding various land surface and ecohydrological processes. Due to the lack of field measurements, different methods have been proposed to estimate RZSM, including the use of exponential filters to predict RZSM from remotely sensed near surface soil moisture data. However, inconsistent findings about the controls on the optimal characteristic time length T opt , which is used in the exponential filter method, have been reported in the literature. To reconcile these inconsistent findings and further improve the use of the method, the impacts of soil properties and climatic conditions on T opt were assessed in this study using observed and modelled soil moisture datasets. Daily soil moisture data, daily meteorological records, and soil properties were retrieved from the Automated Weather Data Network (AWDN) and the Soil Climate Analysis Network (SCAN) within the continental United States. Data from the AWDN stations showed that T opt was mostly controlled by soil texture (e.g., a negative correlation with the sand fraction and a positive one with the clay fraction) as compared to climatic conditions. However, at SCAN stations, T opt was mostly affected by precipitation ( P ), and no significant correlation was found between T opt and soil texture. The difference in controlling factors between ADWN and SCAN stations can be largely attributed to the higher spatial variability in P across the SCAN stations, which overrode the impacts of soil properties on T opt . A 1-D vadose zone model was also utilized to simulate soil moisture at selected SCAN sites using a generated soil hydraulic parameter dataset. The simulation results further demonstrated the negative relationship between T opt and P observed for the SCAN stations. Moreover, the simulation results revealed that T opt was larger under vegetated conditions than under bare surface conditions. Under the same climatic conditions at each simulated site, which could be deemed as reduced variability in P , significant correlations existed between T opt and van Genuchten parameters. In particular, T opt was shown to be smaller for coarser soils, which was consistent with the results observed from AWDN stations. The findings of this study offer additional insights into the use of the exponential filter method for estimating RZSM from near surface soil moisture measurements. [ABSTRACT FROM AUTHOR]

Time-varying coefficient models are widely used in longitudinal data analysis. These models allow the effects of predictors on response to vary over time. In this article, we consider a mixed-effects time-varying coefficient model to account for the within subject correlation for longitudinal data. We show that when kernel smoothing is used to estimate the smooth functions in time-varying coefficient models for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases might lead to erroneous conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and an analysis of Baltimore MACS data. [ABSTRACT FROM AUTHOR]

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples. [ABSTRACT FROM AUTHOR]

While there has been a lot of attention paid recently to big data, in which data is written to massive repositories for later analysis, there also is a rapidly increasing amount of data available in the form of data streams or events. Data streams typically represent very recent measurements or current system states. Events represent things that happen, often in the context of computer processing. When processing data streams or events, we often need to make decisions in real time. Complex event processing (CEP) is an important area of computer science that provides powerful tools for processing events and analyzing data streams. CEP deals with events that can be comprised of other events and can model complex phenomena like a user's interactions with a web site or a stock market crash. In the current literature, CEP is almost entirely deterministic, that is, it does not account for randomness or rely on statistical methods. However, statistics and machine learning have a critical role to play in the use of data streams and events. Also, understanding how CEP works is critical to analyzing data based on complex events. When processing data streams, a distinction must be made between analysis, the human activity in which we try to gain understanding of an underlying process, and decision making, in which we apply knowledge to data to decide what action to take. Useful statistical techniques for data streams include smoothing, generalized additive models, change point detection, and classification methods. [ABSTRACT FROM AUTHOR]

We propose a data-driven, nonparametric approach to reformulate (conditional) individual and joint chance constraints with right-hand side uncertainty into algebraic constraints. The approach consists of using kernel smoothing to approximate unknown true continuous probability density/distribution functions. Given historical data for continuous univariate or multivariate random variables (uncertain parameters in an optimization model), the inverse cumulative distribution function (quantile function) and the joint cumulative distribution function are estimated for the univariate and multivariate cases, respectively. The approach relies on the construction of a confidence set that contains the unknown true distribution. The distance between the true distribution and its estimate is modeled via ϕ -divergences. We propose a new way of specifying the size of the confidence set (i.e., the ϕ -divergence tolerance) based on point-wise standard errors of the smoothing estimates. The approach is illustrated with a motivating and an industrial production planning problem with uncertain plant production rates. [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 study non-negative solutions to the chemotaxis system under no-flux boundary conditions in a bounded planar convex domain with smooth boundary, where f and S are given parameter functions on Ω × [0, ∞)2 with values in [0, ∞) and ℝ2×2, respectively, which are assumed to satisfy certain regularity assumptions and growth restrictions. Systems of type (⋆), in the special case reducing to a version of the standard Keller-Segel system with signal consumption, have recently been proposed as a model for swimming bacteria near a surface, with the sensitivity tensor then given by , reflecting rotational chemotactic motion. It is shown that for any choice of suitably regular initial data (u0, v0) fulfilling a smallness condition on the norm of v0 in L∞(Ω), the corresponding initial-boundary value problem associated with (⋆) possesses a globally defined classical solution which is bounded. This result is achieved through the derivation of a series of a priori estimates involving an interpolation inequality of Gagliardo-Nirenberg type which appears to be new in this context. It is next proved that all corresponding solutions approach a spatially homogeneous steady state of the form (u, v) ≡ (μ, κ) in the large time limit, with μ := fΩu0 and some κ ≥ 0. A mild additional assumption on the positivity of f is shown to guarantee that κ = 0. Finally, numerical solutions are presented which suggest the occurrence of wave-like solution behavior. [ABSTRACT FROM AUTHOR]

In this article, we extend smoothing splines to model the regression mean structure when data are sampled through a complex survey. Smoothing splines are evaluated both with and without sample weights, and are compared with local linear estimator. Simulation studies find that nonparametric estimators perform better when sample weights are incorporated, rather than being treated as if iid. They also find that smoothing splines perform better than local linear estimator through completely data-driven bandwidth selection methods. [ABSTRACT FROM AUTHOR]

In this article we consider the problem to find a very weak solution $$u \in L^1(\Omega )$$ of Poisson's equation $$- \Delta u = f$$ in a smooth bounded domain $$\Omega \subset {\mathbb {R}}^N$$ for a singular right hand side $$f$$ under Neumann boundary conditions on $$\partial \Omega $$ . We prove a general existence and uniqueness theorem and discuss regularity of very weak solutions. Particularly, we are able to generalize corresponding results for Poisson's problem with $$f \in L^1(\Omega )$$ and Neumann boundary condition $$\frac{\partial u}{\partial n} = \left( -\int \nolimits _\Omega f(x)\,dx\right) \delta _{x_0}$$ for a point $$x_0 \in \partial \Omega $$ to non-integrable $$f$$ with $$f(x)\,|x-x_0| \in L^1(\Omega )$$ . Applications to existence for singular data and properties of boundary Green functions are presented. [ABSTRACT FROM AUTHOR]

Biquadratic (bi-2) splines are the simplest choice for converting a regular quad meshes into smooth tensor-product spline surfaces. Existing methods for blending three, five or more such bi-2 spline surfaces using surface caps consisting of pieces of low polynomial degree suffer from artifacts ranging from flatness to oscillations. The new construction, based on reparameterization of the bi-2 spline data, yields well-distributed highlight lines for a range of challenging test data. The construction uses n pieces of degree bi-4 (bi-3 when n ∈ { 3 , 5 } ) and applies both to primal (Catmull–Clark-like) and dual (Doo–Sabin-like) input layouts. [ABSTRACT FROM AUTHOR]

This paper is motivated by a wide range of background correction problems in gene array data analysis, where the raw gene expression intensities are measured with error. Estimating a conditional density function from the contaminated expression data is a key aspect of statistical inference and visualization in these studies. We propose re-weighted deconvolution kernel methods to estimate the conditional density function in an additive error model, when the error distribution is known as well as when it is unknown. Theoretical properties of the proposed estimators are investigated with respect to the mean absolute error from a “double asymptotic” view. Practical rules are developed for the selection of smoothing-parameters. Simulated examples and an application to an Illumina bead microarray study are presented to illustrate the viability of the methods. [ABSTRACT FROM AUTHOR]

This study evaluates the effects of spatial smoothing on inter-subject correlation (ISC) analysis for FMRI data using the traditional model based analysis as a reference. So far within ISC analysis the effects of smoothing have not been studied systematically and linear Gaussian filters with varying kernel widths have been used without better knowledge about the effects of filtering. Instead, with the traditional general linear model (GLM) based analysis, the effects of smoothing have been studied extensively. In this study, ISC and GLM analyses were computed with two experimental and one simulated block-design datasets. The test statistics and the detected activation areas were compared numerically with correlation and Dice similarity measures, respectively. The study verified that 1) the choice of the filter substantially affected the activations detected by ISC analysis, 2) the detected activations according to ISC and GLM methods were highly similar regardless of the smoothing kernel and 3) the effect of spatial smoothing was mildly smaller on ISC than GLM analysis. Our results indicated that a good selection of the full width at half maximum of the Gaussian smoothing kernel for ISC was slightly larger than double the original voxel size. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose exponential smoothing prediction-based segmentation algorithm. [•] The single exponential smoothing method is used to predict future data elements. [•] The prediction error criterion is proposed to determine segmenting key points. [•] The experiments demonstrate the effectiveness and efficiency of the proposed algorithm. [Copyright &y& Elsevier]

The effects lighting has on health through modulation of circadian rhythms are becoming increasingly well documented. Data are still needed to show how light exposures are influenced by architecture and lighting design and circadian dosimetry analyses should provide duration, phase and amplitude measures of 24 h exposure profiles. Exponential smoothing is used to derive suitable metrics from 24 h light measurements collected from private dwellings. A further application of these modified exposure time series as physiological models of the light drive is discussed. Unlike previous light drive models, the dose rate persists into periods of darkness following exposures. Comparisons to long duration exposure studies suggest this type of persistent light drive model could be incorporated into contemporary physiological models of the human circadian oscillator. [ABSTRACT FROM AUTHOR]

The article begins with the formulation for predictive learning called exponential smoothing forecasting. The exponential smoothing is commonly applied to financial markets such as stock or bond, foreign exchange, insurance, credit, primary and secondary markets. The exponential smoothing models are useful in providing the valuable decision information for investors. Simple and double exponential smoothing models are two basic types of exponential smoothing method. The simple exponential smoothing method is suitable for financial time series forecasting for the specified time period. The simple exponential smoothing weights past observations with exponentially decreasing weights to forecast future values. The double exponential smoothing is a refinement of the simple exponential smoothing model but adds another component which takes into account any trend in the data. The double exponential smoothing is designed to address this type of data series by taking into account any trend in the data. Measurement of the forecast accuracy is described in this article. Finally, the quantitative value of the price per common share forecast using simple exponential smoothing is calculated. The applied recommendations concerning determination of the price per common share forecast using double exponential smoothing are shown in the article. [ABSTRACT FROM AUTHOR]

Highlights: [•] Presence profiles in an office environment are successfully modeled using inhomogeneous Markov chains. [•] As inputs to the Markov chain polynomials and splines of time of day are used to model diurnal dependence. [•] Exponential smoothing of observations is used to model per-sequence dynamics. [•] Simulations using the fitted model show same key features as collected data. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new method for modelling curves with dynamic structures, using a non-parametric approach formulated as a state space model. The non-parametric approach is based on the use of penalised splines, represented as a dynamic mixed model. This formulation can capture the dynamic evolution of curves using a limited number of latent factors, allowing an accurate fit with a small number of parameters. We also present a new method to determine the optimal smoothing parameter through an adaptive procedure, using a formulation analogous to a model of stochastic volatility (SV). The non-parametric state space model allows unifying different methods applied to data with a functional structure in finance. We present the advantages and limitations of this method through simulation studies and also by comparing its predictive performance with other parametric and non-parametric methods used in financial applications using data on the term structure of interest rates. [ABSTRACT FROM PUBLISHER]

Measuring and analyzing time-intensity ( T- I) of sensory attributes is an important subject of sensory analysis. This paper proposes using functional data analysis ( FDA), an emerging field in statistical research, as a new strategy and framework for sensory T- I data analysis. This paper discusses and illustrates how to apply the well-developed FDA techniques and use the available R package 'fda' to analyze sensory T- I data. The analyses include data smoothing, descriptions of functional data, functional regression analysis, functional analysis of variance and permutation tests of functional hypotheses (functional F-tests and t-tests). Some conclusions about applications of FDA to sensory T- I data are reached. Practical Applications The currently used statistical analysis for sensory T- I data is not well developed. There are some limitations of using univariate and multivariate data analyses for sensory T- I data. FDA is a promising alternative. This paper shows some advantages using FDA and the R package 'fda' for the analysis of sensory T- I data. It is expected that the introduction and application of FDA in the sensory field will dramatically improve data analysis for T- I evaluation of sensory attributes. [ABSTRACT FROM AUTHOR]