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Abstract.In this article, we introduce a non parametric regression estimator based on a relative error criterion, for left truncated and right censored data with functional predictors. Left truncation and right censoring are common forms of incomplete data in survival analysis, where the event time of interest is only observed within a certain interval which adds some challenges to the regression task. We establish the asymptotic normality of our estimator and develop a procedure for constructing confidence intervals for the predicted responses. The theoretical results obtained are supported using simulation studies and a real data example from the energy field. [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the local linear k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors of the constructed estimators. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The usefulness of our result for the smoothing parameter automatic selection is discussed. Some simulation studies are carried out to show the finite sample performances of the kNN estimator. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in functional data analysis. [ABSTRACT FROM AUTHOR]

This paper reports on our study of a regularization path algorithm for a regression spline estimator based on B-splines and total variation penalty. The total variation-penalized regression spline estimation method enjoys a spatial adaptation property, since the penalty function enables data-adaptive knot selection. Although the theoretical properties of the related methods have been well established in the literature, the existing implementation algorithms are usually based on techniques with a high computational cost. In particular, the selection of the optimal complexity parameter, required to strike a balance in bias-variance tradeoff, is based on the computationally intensive grid search method. In this study, we propose an efficient path algorithm by formulating an equivalent ℓ 1 penalized optimization problem. The least angle regression algorithm is applied to the reformulated problem to obtain an entire path of the jump size of B-spline derivatives that represents the knot removal condition. Numerical studies based on real and simulated data are provided to illustrate the advantages of the proposed algorithm. The simulation result shows that the proposed algorithm is significantly faster than an existing algorithm. The proposed algorithm has an additional benefit of obtaining an entire regularization path, which can provide additional statistical insights into the given problem. [ABSTRACT FROM AUTHOR]

In the past two decades, model averaging has attracted more and more attention and is regarded as a much better tool to solve model uncertainty than model selection. Compared with the conditional mean regression, the quantile regression serves as a robust alternative and shows a lot more information about the conditional distribution of a response variable. In this paper, we propose a jackknife model averaging procedure that chooses the weights by minimizing a leave-one-out cross-validation criterion function for mixed-data kernel-weighted spline quantile regressions that contain both continuous and categorical regressors when all candidate models are potentially misspecified. We demonstrate the JMA estimator is asymptotically optimal in terms of minimizing the out-of-sample final prediction error. Simulation experiments are conducted to assess the relative finite-sample performance of the proposed JMA method with respect to other model selection and averaging methods. Our JMA method is applied to the wage and house datasets. [ABSTRACT FROM AUTHOR]

In the past 20 years, model averaging has been developed as a better tool than model selection in statistical prediction. Expectile prediction is widely used for modeling data with the heterogeneous conditional distribution. In this article, we introduce a model averaging estimator for additive expectile prediction. The resulting model averaging estimator is shown to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to demonstrate that the performance of our method is better than that of other common model selection and model averaging methods under the finite-sample case. Our method is also verified in the house and wage datasets. [ABSTRACT FROM AUTHOR]

Additive partial linear models with symmetric autoregressive errors of order p are proposed in this paper for modeling time series data. Specifically, we apply this model class to explain the weekly hospitalization for respiratory diseases in Sorocaba, São Paulo, Brazil, by incorporating climate and pollution as covariates, trend and seasonality. The main feature of this model class is its capability of considering a set of explanatory variables with linear and nonlinear structures, which allows, for example, to model jointly trend and seasonality of a time series with additive functions for the nonlinear explanatory variables and a predictor to accommodate discrete and linear explanatory variables. Additionally, the conditional symmetric errors allow the possibility of fitting data with high correlation order, as well as error distributions with heavier or lighter tails than the normal ones. We present the model class and a novel iterative process is derived by combining a P-GAM type algorithm with a quasi-Newton procedure for the parameter estimation. The inferential results, diagnostic procedures, including conditional quantile residual analysis and local influence analysis for sensitivity, are discussed. Simulation studies are performed to assess finite sample properties of parametric and nonparametric estimators. Finally, the data set analysis and concluding remarks are given. [ABSTRACT FROM AUTHOR]

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained. [ABSTRACT FROM AUTHOR]

AbstractWe, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed. [ABSTRACT FROM AUTHOR]

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. 'Semiparametric Zero-Inflated Bernoulli Regression with Applications', Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study. [ABSTRACT FROM AUTHOR]

This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence. [ABSTRACT FROM AUTHOR]

We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate ψ -mixing Markov chains. Some general results on ψ -mixing are given. The Spearman's correlation ρ S and Kendall's τ are provided for the created copula families. Some general remarks are provided for ρ S and τ . A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples. [ABSTRACT FROM AUTHOR]

We propose a covariance ratio measure for symmetry or asymmetry of a probability density function. This measure is constructed by the ratio of the covariance connected with the density function and the distribution function. We first propose a non parametric moment-based estimator of the covariance ratio measure and study its asymptotic results. Next, we consider statistical inference of the covariance ratio measure by using the empirical likelihood method. The empirical likelihood statistic is shown to be asymptotically a standard chi-squared distribution. Last, we study the covariance ratio measure when the random variable is unobserved under the multiplicative distortion measurement errors setting. The density function and the distribution function of the unobserved variable are estimated by using four calibrated variables. Appealing to these estimators, the calibrated covariance ratio measures are proposed and further shown to be asymptotically efficient as if there are no multiplicative distortion effects. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test procedures. These methods are applied to analyze two real datasets for illustration. [ABSTRACT FROM AUTHOR]

In this article, we study the non parametric estimation of some regression curves when the data are observed with additive distortions, and these distortions for unobservable response variables and covariates are connected with a common observed confounding variable. We study the estimates of the non parametric mean function and its first derivative, the variance function, the Sharpe ratio function, and the correlation curve function. We obtain asymptotic normality results for the proposed non parametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyze a QSAR fish toxicity dataset for illustration. [ABSTRACT FROM AUTHOR]

The focus of this article is on studying a partially linear additive model, which is defined using a measurable function ψ : R q → R . The model is given as follows: ψ (Y i) := Y i = Z i ⊤ β + ∑ ℓ = 1 d m ℓ (X ℓ , i) + ε i for 1 ≤ i ≤ n , where Z i = (Z i , 1 , ... , Z i p ) ⊤ and X i = (X 1 , i , ... , X i d ) ⊤ are vectors of explanatory variables, β = (β 1 , ... , β p ) ⊤ is a vector of unknown parameters, m 1 , ... , m d are unknown univariate real functions, and ε 1 , ... , ε n are independent random errors with mean zero, finite variances σε. Additionally, it is assumed that E (ε | X , Z) = 0 almost surely. The main contributions of this article are as follows. First, under certain mild conditions, we establish the asymptotic normality of the non linear additive components of the model. These components are estimated using the marginal integration device with the linear wavelet method. Second, we leverage our main result to construct confidence intervals for the estimated model. [ABSTRACT FROM AUTHOR]

There are many studies aimed at promoting positive lifestyle behaviors to reduce lifetime risk of cancer and related diseases. However, assessing these modifiable behaviors through statistical modeling is challenging because of the multidimensionality of interrelated measurements that may dramatically differ between at-risk individuals. Taking into account this heterogeneity while considering the multidimensionality of behavior changes is fundamental to tailoring interventions to their needs. Biomarkers that identify high-risk individuals may help validate proximal measures, but the number of validated methods that link biomarkers to multiple behavioral measurements by determining their dynamic relations with disease risks is limited to just a few, since it requires an advanced statistical methodology to address challenges in analyzing biomarker data, including left-censoring due to limits of detection. To address these challenges, we propose a method that constructs a quantile-specific weighted index of multiple behavioral measurements. Under the quantile regression framework, the proposed method renders a multidimensional view of risk-specific behavioral patterns by connecting them with biomarker levels to provide better insights into heterogeneous behavioral profiles among at-risk populations. We evaluate performances of the proposed method through simulations, and illustrate its applications to the Tu Salud ¡Sí Cuenta! data by examining behavior changes among Mexican-American adults. [ABSTRACT FROM AUTHOR]

We study benign overfitting in the setting of nonparametric regression under mean squared risk, and on the scale of Hölder classes. We construct a local polynomial estimator of the regression function that is minimax optimal on a Hölder class with any given smoothness, and that is a continuous function interpolating the set of observations with high probability. The key element of the construction is the use of singular kernels. Moreover, we prove that adaptation to unknown smoothness is compatible with benign overfitting. Namely, we construct a continuous and interpolating local polynomial estimator attaining the minimax optimal rate in L 2 adaptively to the unknown Hölder smoothness. Our results highlight the fact that interpolation can be fundamentally decoupled from bias-variance tradeoff in the problem of nonparametric regression. [ABSTRACT FROM AUTHOR]

This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression. [ABSTRACT FROM AUTHOR]

Abstract.To check the significance of the regression coefficients in the linear component of high-dimensional partial linear models, we proposed some projection-based test statistics. These test statistics are connected with U-statistics of order two and they are applicable for diverging dimensions and heteroscedastic model errors. By using the martingale central limit theorem, we show the asymptotic normalities of the proposed test statistics under the null hypothesis and local alternative hypotheses. The performance of test statistics are evaluated by simulation studies. The simulation results show that the proposed test statistics are powerful and have the correct type-I error asymptotically under the null hypothesis. [ABSTRACT FROM AUTHOR]

Abstract.This study delves into the conditional mode estimation of a randomly censored scalar response variable operating within the framework of strong mixing conditions. We introduce a kernel-based estimator for the conditional mode function. The principal contribution of this investigation lies in the derivation of the asymptotic distribution and the strong rate of convergence of the newly proposed estimators. These findings are established under a set of fairly comprehensive structural assumptions governing the underlying models. Additionally, we conduct a series of simulation studies to showcase the finite sample performance characteristics of the proposed estimator. [ABSTRACT FROM AUTHOR]

We address the semiparametric challenge of identifying and estimating generalized additive partial linear models with nonignorable missingness in the response. Identifiability is ensured under instrumental variable assumption that there is an instrumental covariate related to the prospensity but unrelated to the response variable, or the assumption that the conditional score function is linear in the response variable. We propose a new estimating equation for the prospensity by taking expectation of the unobservable part on a linear combination of all covariates rather than the covariates themselves. This estimating equation does not suffer from the typical curse of dimensionality. Then the unknown nonparametric function is approximated by polynomial spline basis functions and we construct estimating equations for mean of response based on the inverse probability weighting. Under some regular conditions, we establish asymptotic normality of the proposed estimators for parametric components and consistency of the estimators of nonparametric functions. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. The proposed method is applied to analyze the household income dataset from the Chinese Household Income Project Survey 2013. [ABSTRACT FROM AUTHOR]

In recent years, the direction has turned to non-stationary time series. Here the situation is more complicated: it is often unclear how to set down a meaningful asymptotic for non-stationary processes. For this reason, the theory of locally stationary processes arose, and it is based on infill asymptotics created from non-parametric statistics. The present paper aims to develop a framework for inference of locally stationary functional time series based on the so-called conditional U-statistics introduced by Stute (Ann Probab 19:812–825, 1991), and may be viewed as a generalization of the Nadaraya-Watson regression function estimates. In this paper, we introduce an estimator of the conditional U-statistics operator that takes into account the nonstationary behavior of the data-generating process. We are mainly interested in establishing weak convergence of conditional U-processes in the locally stationary functional mixing data framework. More precisely, we investigate the weak convergence of conditional U-processes when the explicative variable is functional. We treat the weak convergence when the class of functions is bounded or unbounded, satisfying some moment conditions. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The theoretical results established in this paper are (or will be) critical tools for further functional data analysis developments. [ABSTRACT FROM AUTHOR]

Abstract.In this article, our central focus is to investigate the non parametric estimator of the probability density or mass function of a data stream by using the general family of kernels, also called multivariate associated kernels. Being able to estimate categorial, count, discrete, and (semi)continuous distributions, these multivariate associated kernel estimators unify several particular cases. Within this framework, we first introduce a recursive estimator for non classical associated kernels. Under reasonable assumptions, we subsequently exhibit their asymptotic results, such as the local uniform Lq-consistency, the pointwise asymptotic normality and finally the strong global consistency. Illustrative examples of associated kernels are revisited. [ABSTRACT FROM AUTHOR]

A Partially linear mixed effects model relating a response Y to predictors $ (X,Z,T) $ (X , Z , T) with the mean function $ X^{T}\beta +Zb+g(T) $ X T β + Zb + g (T) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper. [ABSTRACT FROM AUTHOR]

This paper develops a new nonparametric estimator of the scalar-on function modal regression that is used to analyse the co-variability between a functional regressor and a scalar output variable. The new estimator inherits the smoothness of the kernel method and the robustness of the quantile regression. We assume that the functional observations are structured as a strong mixing functional time series data and we establish the almost complete consistency (with rate) of the constructed estimator. A discussion highlighting the impact of this new estimator in nonparametric functional data analysis is also given. The usefulness of this new estimator is shown using an artificial data example. [ABSTRACT FROM AUTHOR]

Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse problems, sensitivity analysis, and surrogate models’ design, especially when in presence of high-dimensional parametrized systems. In this work we propose a new method called local active subspaces (LAS), which explores the synergies of active subspaces with supervised clustering techniques in order to carry out a more efficient dimension reduction in the parameter space. The clustering is performed without losing the input–output relations by introducing a distance metric induced by the global active subspace. We present two possible clustering algorithms: K-medoids and a hierarchical top–down approach, which is able to impose a variety of subdivision criteria specifically tailored for parameter space reduction tasks. This method is particularly useful for the community working on surrogate modelling. Frequently, the parameter space presents subdomains where the objective function of interest varies less on average along different directions. So, it could be approximated more accurately if restricted to those subdomains and studied separately. We tested the new method over several numerical experiments of increasing complexity, we show how to deal with vectorial outputs, and how to classify the different regions with respect to the LAS dimension. Employing this classification technique as a preprocessing step in the parameter space, or output space in case of vectorial outputs, brings remarkable results for the purpose of surrogate modelling. [ABSTRACT FROM AUTHOR]

We are mainly concerned with the partially linear additive model defined for a measurable function ψ : R q → R , by ψ (Y i) : = Y i = Z i ⊤ β + ∑ l = 1 d m l (X l , i) + ε i for 1 ≤ i ≤ n , where Z i = (Z 1 , i , ... , Z p , i) ⊤ and X i = (X 1 , i , ... , X i , d) ⊤ are vectors of explanatory variables, β = (β 1 , ... , β p) ⊤ is a vector of unknown parameters, m 1 , ... , m d are unknown univariate real functions, and ε 1 , ... , ε n are independent random errors with mean zero, finite variances σ ε and E (ε | X , Z) = 0 a.s. Under some mild conditions, we present a sharp uniform-in-bandwidth limit law for the nonlinear additive components of the model estimated by the marginal integration device with the kernel method. We allow the bandwidth to varying within the complete range for which the estimator is consistent. We provide the almost sure simultaneous asymptotic confidence bands for the regression functions. [ABSTRACT FROM AUTHOR]

In the last few years, frequentist model averaging has received more and more attention. However, the majority of related work focuses on the parametric model setup and devotes more energy to different mean structures but ignores the form of variance. In this paper, we consider a regression model with the mean being a varying-coefficient model and the variance being multiplicative heteroscedasticity and introduce a model averaging approach that uses the B-spline smoothing method to estimate unknown coefficient functions and obtains the estimators of unknown parameters in both the mean and variance functions of the model by the maximum likelihood method. The resulting model averaging estimator is proved to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to compare the performance of our method with that of other common heteroscedasticity-robust model selection and model averaging methods under the finite-sample case. Our method is also verified in a real dataset. [ABSTRACT FROM AUTHOR]

Composite quantile regression methods have been shown to be effective techniques in improving the prediction accuracy. In this article, we propose a Bayesian weighted composite quantile regression estimation procedure to estimate unknown regression coefficients and autoregressive parameters in the linear regression models with autoregressive errors. A Bayesian joint hierarchical model is established using the working likelihood of the asymmetric Laplace distribution. Adaptive Lasso-penalized type priors are used on regression coefficients and autoregressive parameters of the model to conduct inference and variable selection simultaneously. A Gibbs sampling algorithm is developed to simulate the parameters from the posterior distributions. The proposed method is illustrated by some simulation studies and analyzing a real data set. Both simulation studies and real data analysis indicate that the proposed approach performs well. [ABSTRACT FROM AUTHOR]

AbstractWe consider the estimation of Pearson correlation coefficient when two continuous variables can not be directly observed but measured with multiplicative distortion measurement errors. Different from the identifiability conditions for the distortion functions in literature, we propose a new estimation method of Pearson correlation coefficient by transforming the linear model between two variables into varying coefficient models, a moment-based estimator of the Pearson correlation coefficient is proposed. This method can deal with the non-independence condition between the confounding variable and the unobserved variables. We study the asymptotic results of these proposed estimators, and we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for the use of smoothing techniques that annihilate the noise. At the same time, imposing the smoothness assumption excludes a considerable range of stochastic processes, most notably diffusion processes. Under perfect observation of the sample paths, such processes would not need to be excluded from the realm of functional data analysis. In this paper, we introduce a careful modification of existing methods, dubbed the 'reflected triangle estimator', and show that this allows for the functional data analysis of processes with nowhere differentiable sample paths, even when these are discretely and noisily observed, including under irregular and sparse designs. Our estimator matches the established rates of convergence for processes with smooth paths, and furthermore attains the same optimal rates as one would get under perfect observation. Thus, with reflected triangle estimation, the scope of applicability of much of the methodology developed for discretely/irregularly/noisily/sparsely sampled functional data is considerably extended. By way of simulation it is shown that the advantages furnished are reflected in practice, hinting at potential closer links with the field of diffusion inference. [ABSTRACT FROM AUTHOR]

Tolerance intervals in regression allow the user to quantify, with a specified degree of confidence, bounds for a specified proportion of the sampled population when conditioned on a set of covariate values. While methods are available for tolerance intervals in fully-parametric regression settings, the construction of tolerance intervals for nonparametric regression models has been treated in a limited capacity. This paper fills this gap and develops likelihood-based approaches for the construction of pointwise one-sided and two-sided tolerance intervals for nonparametric regression models. A numerical approach is also presented for constructing simultaneous tolerance intervals. An appealing facet of this work is that the resulting methodology is consistent with what is done for fully-parametric regression tolerance intervals. Extensive coverage studies are presented, which demonstrate very good performance of the proposed methods. The proposed tolerance intervals are calculated and interpreted for analyses involving a fertility dataset and a triceps measurement dataset. [ABSTRACT FROM AUTHOR]

In Selk, L., and Gertheiss, J. [(2022), 'Nonparametric Regression and Classification with Functional, Categorical, and Mixed Covariates', Advances in Data Analysis and Classification] a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, so that both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are studied. A uniform convergence rate for the regression / classification estimator is given. It is further shown that a data-driven least squares cross-validation method can asymptotically remove irrelevant noise variables automatically. [ABSTRACT FROM AUTHOR]

This paper considers nonlinear regression models when neither the response variable nor the covariates can be directly observed, but are measured with exponential parametric distortion measurement errors. To estimate parameters in the distortion functions, we propose nonlinear least squares and weighted nonlinear least squares estimation methods under two identifiability conditions. After obtaining calibrated variables, the nonlinear least squares based estimators are proposed to estimate the parameters in the regression model. We studied the asymptotic results of estimators, especially we discuss the difference between the parametric calibrations and nonparametric calibrations. The latter is conducted as if the parametric structures in distortion functions are unknown. Simulation studies demonstrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a parametric hypothesis test of the multiplicative distortion model under the exponentially distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. Firstly, some new test statistics are proposed to checking the exponential distribution assumption without distortion effects. Next, we proposed several test statistics when the variable is distorted in the multiplicative fashion. For the latter, the proposed test statistics automatically eliminate the distortion effects involved in the unobserved variable. The proposed test statistics with or without distortions are all asymptotical free, and the asymptotic null distribution of the test statistics are obtained with known asymptotic variances. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. These methods are applied to analyze four real datasets for illustrations. [ABSTRACT FROM AUTHOR]

Shape, as an intrinsic concept, can be considered as a source of information in some statistical analysis contexts. For instance, one of the important topics in morphology is to study the shape changes along time. From a topological viewpoint, shape data are points on a particular manifold and so to construct a longitudinal model for treating shape variation is not as trivial as thought. Unlike using the common parametric models to do such a task, we invoke Procrustes analysis in the context of a nonparametric framework and propose a simple, yet useful, model to deal with shape changes. After conveying the problem into the nonparametric regression model, we utilize the weighted least squares method to estimates the related parameters. Also, we illustrate implementing this new model in simulation studies and analyzing two biological data sets. Our proposed model shows its superiority while compared with other counterpart models. [ABSTRACT FROM AUTHOR]

Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (J Am Stat Assoc 101(475):980–990, 2006. https://doi.org/10.1198/016214506000000672) in the spirit of Tokdar and Kadane (Bayesian Anal 7(1):51–72, 2012. https://doi.org/10.1214/12-BA702). We offer a directly interpretable parametric model specification for QAR. Further, we offer a pth-order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Aragón, Spain. [ABSTRACT FROM AUTHOR]