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This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated. [ABSTRACT FROM AUTHOR]

Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the estimation problem about the regression coefficients of a multivariate regression model with measurement errors under some uncertain restrictions. Specifically, we propose the unrestricted estimator (UE) and three restricted estimators (REs), and prove that they are all consistent for the true coefficients. We derive the asymptotic distributions of the proposed estimators under the sequence of local alternative restrictions. We also propose shrinkage estimators (SEs) to address the problem of the uncertainty of the restrictions. In addition, we establish the asymptotic distributional risk (ADR) of the proposed estimators and compare the risk performance of these estimators. It is established that the REs perform better than the UE only near the restriction, while they perform poorly as one moves farther away from the restriction. We also prove that SEs dominate the UE. These theoretical results are confirmed by simulations. [ABSTRACT FROM AUTHOR]

For the functional linear models in which the dependent variable is functional and the predictors are scalar, robust regularization for simultaneous variable selection and regression parameter estimation is an important yet challenging issue. In this paper, we propose two types of regularized robust estimation methods. The first estimator adopts the ideas of reproducing kernel Hilbert space, least absolute deviation and group Lasso techniques. Based on the first method, the second estimator applies the pre-whitening technique and estimates the error covariance function by using functional principal component analysis. Simulation studies are conducted to examine the performance of the proposed methods in small sample sizes. The method is also applied to the Canadian weather data set, which consists of the daily average temperature and precipitation observed by 35 meteorological stations across Canada from 1960 to 1994. Numerical simulations and real data analysis show a good performance of the proposed robust methods for function-on-scalar models. [ABSTRACT FROM AUTHOR]

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries. [ABSTRACT FROM AUTHOR]

In this paper, the sufficient and necessary conditions for the strong consistency of least squares estimators in simple linear EV regression models are proved under widely orthant dependent random errors. The results obtained in the paper improve and extend some existing ones in the literature. Simulation studies are also carried out to support the consistency of the estimators under dependence assumption and finite samples. [ABSTRACT FROM AUTHOR]

High-dimensional data often display heteroscedasticity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inference for the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates heteroscedasticity. This paper aims to simultaneously carry out variable selection and heteroscedasticity identification for the linear location-scale model under a unified framework. We develop a regularized multiple quantile regression approach simultaneously identifying the heteroscedasticity, seeking common features of quantile coefficients and eliminating irrelevant variables. We also establish the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, showing that it is able to identify the covariates that affect the variability of the response. We further apply the proposed method to analyse the Wage data. [ABSTRACT FROM AUTHOR]

In statistics, regression analysis is a method for predicting a target variable by establishing the optimal linear relationship between the dependent and independent variables. The ordinary least squares estimator (OLSE) is the optimal estimation method in classical regression analysis based on the Gauss–Markov theorem if the essential assumptions of normality, independence of error terms, and little or no multicollinearity in the covariates are satisfied. OLSE is profoundly affected by the collinearity between explanatory variables and outlier problems. Therefore, we require resilient strategies to resolve these challenges. Robust stochastic ridge regression is an alternative optimization problem to least squares regression when data are simultaneously contaminated by anomalies, influential observations, and multicollinearity. To combat outliers and multicollinearity problems, a robust stochastic ridge regression estimator based on the least squares trimmed method is proposed in this paper. Using simulated and real data sets, the efficacy of the proposed method with correlated and uncorrelated errors is then evaluated. [ABSTRACT FROM AUTHOR]

The ordinary least squared and ridge regression estimators in a linear regression model are sensitive to outliers in the y-variable. In such situations, ridge M-estimators are widely used which are robust to the y-variable outliers and overcome the multicollinearity problem. Similar to ridge regression, to lower the mean square error (MSE) of ridge M-estimators, it is crucial to select the most robust ridge parameter. The performance of existing estimators for the estimation of robust ridge parameters deteriorates when the degree of multicollinearity, error variance, and y-variable outliers increases from moderate to high. In this paper, some new robust ridge M-estimators have been proposed. The efficiency of the new estimators has been compared through a Monte Carlo simulation study. Based on the MSE criterion, the new estimators outperform existing estimators. A numerical example has been provided to illustrate the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a penalized weighted quantile estimating equations (PWQEEs) method to obtain sparse, robust and efficient estimators for the quantile regression with longitudinal data. The PWQEE incorporates the within correlations in the longitudinal data by Gaussian copulas and can also down-weight the high leverage points in covariates to achieve double-robustness to both the non-normal distributed errors and the contaminated covariates. To overcome the obstacles of discontinuity of the PWQEE and nonconvex optimization, a local distribution smoothing method and the minimization–maximization algorithm are proposed. The asymptotic properties of the proposed method are also proved. Furthermore, finite sample performance of the PWQEE is illustrated by simulation studies and a real-data example. [ABSTRACT FROM AUTHOR]

Varying coefficient models have been studied for many years, and local kernel estimation is an important method to estimate the coefficient functions. Since same bandwidth parameter is used for each coefficient function, local kernel estimation is not effective when the degree of smoothness is different for each coefficient function. In this paper, a new global estimation method based on kernel function and backfitting is proposed. In this method, different bandwidth parameters can be used for each coefficient function to improve the estimation accuracy, and asymptotic properties of the estimators are proved. To reduce the computational complexity, an adaptive global estimation method, which is based on an estimation of the bandwidth ratio and has only one bandwidth parameter to be selected, is proposed. Simulation results show that the proposed methods work well, and two real data examples further demonstrate the potential of the proposed methods. [ABSTRACT FROM AUTHOR]

Multivariate regression models are helpful in many fields. However, independent variables (covariates or predictors) could be measured with error. That implies the necessity of considering a new kind of model called Multivariate Regression Models with Measurement Error (MRMMEs). This paper aims to carry out a statistical analysis of these models. We include estimation, hypothesis testing, model assessment, and influence diagnostics. Furthermore, besides considering the classical assumption of the normal distribution, we use maximum likelihood for the whole inference process. Finally, we study the developed approach's performance through simulation experiments and re-analyze the human lung function dataset presented in the literature to illustrate the methodology. [ABSTRACT FROM AUTHOR]

A case-cohort design offers an economical way of investigating an association between exposure variables and risks of disease outcomes compared to a large-scale full cohort study. A stratified sampling in such designs based on the information available for the entire cohort is often considered for improving efficiencies of estimators. In this paper, we consider fitting censored quantile regression models for competing risks data arising from stratified case-cohort designs. We model quantiles for cumulative incidence functions that provide desirable interpretation for competing risks data and flexible ways of assessing covariates effects. For estimation of regression parameters, we consider weighted estimating equations with two-types of weights: the inverses of censoring probabilities and sampling probabilities to account for censoring in competing risks data and biased features in stratified case-cohort samplings, respectively. An induced smoothing approach is applied to obtain computationally more reliable estimates. The resulting estimating functions are smooth in regression parameters, so standard numerical algorithms for point estimation can be readily applied and variances can be estimated via a closed-form expression or computationally efficient resampling method. An iterative algorithm is proposed to simultaneously estimate regression parameters and their variances. Asymptotic properties of the proposed estimators are established. The finite sample properties of the proposed estimators are investigated through extensive simulation studies. They perform reasonably well under practical settings considered. The proposed methods are illustrated with Hodgkin's disease data. [ABSTRACT FROM AUTHOR]

Different regression models that use circular data supported on the unit circle are rare. Regression parameters for circular data have mostly been estimated using the least-squares method. This paper addresses multicollinearity between the circular regressors. The ridge estimator is suggested as an alternative to the least-squares estimator in circular-linear regression model. The models fitted by the circular least-squares and circular ridge estimators are compared on real and simulated datasets. The mean squared error and the coefficient of determination are used to assess the models' adequacy. The findings demonstrated that the fitted models might not be significant if the circularity of the data is ignored. Circular regression on circular data shows the model to be significant. Although the two estimators' coefficients of determination for circular models are quite close, the circular ridge estimator with the optimum biasing parameter has a smaller scalar mean square error than the circular least-squares estimator. [ABSTRACT FROM AUTHOR]

Recently the shape-restricted inference has gained popularity in statistical and econometric literature to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotone increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modelled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data-driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit. [ABSTRACT FROM AUTHOR]

This paper is concerned with composite quantile regression for partially linear varying-coefficient models with heteroscedasticity when data are right censored and censoring indicators are missing at random. We construct estimators of parametric regression coefficients and nonparametric varying-coefficient functions in the proposed models based on regression calibration, imputation and inverse probability weighted approaches. The asymptotic normality of the proposed estimators is proved. Meanwhile, an adaptive LASSO penalized variable selection method and its oracle property are considered. We also demonstrate the performance of the proposed estimation method and variable selection procedure through comprehensive simulations and a real-data application. [ABSTRACT FROM AUTHOR]

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be sensitive to outliers. To overcome such problem, robust Bayesian regression models have been proposed in recent years. In this paper, we consider the robust and efficient estimation for the Bayesian Huberized lasso regression in fully Bayesian perspective. A new posterior computation algorithm for the Bayesian Huberized lasso regression is proposed. The proposed approximate Gibbs sampler is based on the approximation of full conditional distribution and it is possible to estimate a tuning parameter for robustness of the pseudo-Huber loss function. Some theoretical properties of the posterior distribution are also derived. We illustrate performance of the proposed method through simulation studies and real data examples. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of variance estimation of predictions obtained from a subsampling-based ensemble estimator, such as subbagging and sub-random forest. We first recognize that a subsampling-based ensemble can be written as an infinite-order U-statistic of degree k n , where k n is the subsample size that may depend on the learning sample size n. As a result, one can study the uncertainty of predictions obtained from a subsampling-based ensemble under a U-statistic framework, such as approximating its asymptotic variance. However, existing methods used to estimate the asymptotic variance relies on some regularity conditions. In addition, they tend to yield variance estimations with large bias in finite sample scenarios. Motivated by the work of Wang and Lindsay (2014), we propose to construct an unbiased variance estimator for a subsampling-based ensemble. It is efficient to realize with the help of a partition-resampling scheme. We show by simulation studies that the proposed variance estimator yields better performance in terms of mean, standard deviation, and mean squared error compared to both the infinitesimal jackknife and internal variance estimation methods under either a simple linear regression model or a multivariate adaptive regression splines model. Furthermore, we present how to construct an asymptotic confidence interval for the expected prediction at a given test instance using the proposed variance estimator, and compare its coverage probability to that of competing methods. In the end, we demonstrate the practical applications of the methodology using two real data examples. [ABSTRACT FROM AUTHOR]

This paper develops a bias correction scheme for reparametrized inverse gamma regression models with varying precision [Bourguignon M, Gallardo DI. Reparametrized inverse gamma regression models with varying precision. Stat Neerl. 2020;74(4):611–627], which is tailored to situations where the response variable has an asymmetrical shape on the positive real line. In particular, we discuss maximum-likelihood estimation for the model parameters and derive closed-form expressions for the first-order bias of the estimators. The expressions derived are simple and only require the definition of a few matrices. This enables us to obtain corrected estimators that are approximately unbiased. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed corrected estimators. Finally, we apply the results obtained in three real-world datasets. This paper contains Supplementary Material. [ABSTRACT FROM AUTHOR]

The classic F-test and z-test can fail for high-dimensional regression models. This paper addresses this problem, especially for the case where the covariates contain a latent factor structure. We first use a new technique, the cross-section averages (CSA) of covariates, to estimate the latent factors. We then develop two F-type tests, namely, the Wald test and the F-test, to assess the overall significance of covariates. If the covariates are tested jointly significant, we next carry out a CSA-based z-test to sequentially test the significance of covariates one at a time. Compared with the existing approaches in the literature, which often use principal component analysis (PCA) to estimate the latent factors, the new tests do not depend on the accurate estimation of the unknown degrees of freedom, or on the acquisition of unknown eigenvalues. Therefore, they can reduce the uncertainty arising from the estimation of unknown quantities. We show the power and model selection consistency of these tests and propose a follow-up ratio-type test to further control the model size. Numerical simulations and a real data analysis show the competitive performance of these CSA-based tests. [ABSTRACT FROM AUTHOR]

In the paper, the central limit theorem for asymptotically negatively associated (ANA, for short) random variables is established. As an application, we consider the nonparametric regression model with repeated measurements: y (j) (x i) = g (x i) + e (j) (x i) , where y (j) (x i) is the jth response at the point x i , x i 's are known fixed design points, and g (⋅) is an unknown Borel measurable function defined on A = [ 0 , 1 ]. Under some general conditions, we study the asymptotic normality of the wavelet estimator of g (⋅) under ANA random errors. The obtained results generalize the corresponding ones for NA random variables. Finally, we will provide the simulation study to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present three empirical likelihood (EL)-based inference procedures to construct confidence intervals for quantile regression models with longitudinal data. The traditional EL-based method suffers from an under-coverage problem, especially in small sample sizes. The proposed modified EL-based non-parametric methods including adjusted empirical likelihood (AEL), the transformed empirical likelihood (TEL), and the transformed adjusted empirical likelihood (TAEL) exhibit good finite sample performance over other existing procedures. Simulations are conducted to compare the performances of the proposed methods with the other methods in terms of coverage probabilities and average lengths of confidence intervals under different scenarios. [ABSTRACT FROM AUTHOR]

In testing an overall null hypothesis, it does not matter whether to permute the response variables (Y) while keeping the predictors fixed or to permute the predictor variables (X) while keeping the response variables fixed. However, in weighted (univariate and multivariate) regression and in partial tests these options yield different results. This paper defines and evaluates by simulation ordinary and standardized versions of X- and Y-permutation for tests which encompass the existing Double Semi-Partialling, here called Collins-Dekker, and Freedman-Lane permutation methods. When the error variance is inversely proportional to the weights, the standardized permutation methods (which use standardized residuals) are most powerful, as expected, but otherwise they can be extremely liberal. In contrast, ordinary X-permutation (which permutes the residuals of X given any covariates 'as is') is by far the most robust against variability in the weights and against the error variance-weight relationship and is thus recommended for general use. [ABSTRACT FROM AUTHOR]

Classification and clustering methods based on univariate functions have been well developed. Recent work has extended the techniques to the domain of bivariate functions by incorporating the techniques based on mixtures of spatial spline regression with mixed-effects models. An Expectation Maximization (EM) algorithm is implemented to facilitate model inference. In this paper, we further extend the mixtures of spatial spline regression with mixed-effects model under the Bayesian framework to accommodate streaming image data. First, we derive a Markov chain Monte Carlo (MCMC) algorithm as an alternative approach to the EM algorithm to make inference on the model. However, MCMC is not scalable to streaming image data since it requires all observed information to update the posterior distribution of the parameters. To tackle this issue, we propose a sequential Monte Carlo (SMC) algorithm to analyse online fashion image data. The existence of model sufficient statistics improves the efficiency of the proposed online SMC algorithm. Instead of saving all batch data for inference, we only require storage of the model sufficient statistics and every data point is only used once, which is well suited for large-scale stream type data. In addition, the proposed algorithm provides an unbiased estimator of the marginal likelihood as a by-product of the approach, which can be used for model selection. Numerical experiments are used to demonstrate the effectiveness of our method. Our implementation is available at . [ABSTRACT FROM AUTHOR]

Models dealing with ordinal multinomial(OM) variables have drawn much attention in regression analysis. Studies on the ordinal response variable have been solidly established and widely applied. However, few studies have investigated generalized linear models with OM covariates, especially in high-dimensional situations. For this problem, the detection of pseudo categories for the OM covariates and the selection of other important covariates need to be concerned simultaneously. This paper proposes an L 1 -norm penalized estimation procedure to detect pseudo categories of OM covariates in high-dimensional( p n ≤ n , p n = O (n σ) , 0 < σ ≤ 1)) Cox models. The estimation approach is based on the combination of a transformation method of dummy variables and the penalized partial likelihood. Theoretical properties, such as consistency and oracle property of the proposed estimators, are rigorously established under some regularity conditions. The performance of the proposed method is illustrated by analyses on both simulated data and real data. [ABSTRACT FROM AUTHOR]

This paper studies a regression with multiple functional predictors and a scalar response. The proposed model, which we called multivariate functional generalized additive model (mFGAM), extends the usual linear regression model in two key respects. First, mFGAM uses group minimax concave penalty (gMCP) to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, mFGAM extends beyond the standard linear regression setting to fit general non-linear additive models, and mFGAM is more flexible than multivariate functional generalized linear model (mFGLM). This model is different from McLean et al. [Functional generalized additive models. J Comput Graph Stat. 2014;23(1):249–269.] since their model cannot deal with the situation where the number of parameters is bigger than the sample size. The simulation studies and the application are performed to demonstrate the accuracy and stability of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, based on the properties of slowly varying functions and the de Bruijn conjugates, we establish general results on complete moment convergence for randomly weighted sums of m-asymptotic negatively associated random variables. These results are applied to the bootstrap sample means and nonparametric regression models with random design. Simulations to study the numerical performance of the consistency for the nearest neighbour weight function estimator in non parametric regression model with random design and bootstrap sample means are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalized logistic regression model. We propose a Pólya–Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The algorithm performance is tested on simulated data. Furthermore, the methodology is applied to two different real datasets, where we demonstrate that the Pólya–Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches. [ABSTRACT FROM AUTHOR]

The modelling of censored survival data is based on different estimations of the conditional hazard function. When survival time follows a known distribution, parametric models are useful. This strong assumption is replaced by a weaker in the case of semiparametric models. For instance, the frequently used model suggested by Cox is based on the proportionality of hazards. These models use non-parametric methods to estimate some baseline hazard and parametric methods to estimate the influence of a covariate. An alternative approach is to use smoothing that is more flexible. In this paper, two types of kernel smoothing and some bandwidth selection techniques are introduced. Application to real data shows different interpretations for each approach. The extensive simulation study is aimed at comparing different approaches and assessing their benefits. Kernel estimation is demonstrated to be very helpful for verifying assumptions of parametric or semiparametric models and is able to capture changes in the hazard function in both time and covariate directions. [ABSTRACT FROM AUTHOR]

Poisson log-linear regression model is commonly used for analysing count data. Valid inference based on this model can be drawn when the mean and variance of the data are equal. However, in practice variance of responses is often much greater than the mean of the responses, known as over-dispersion. Also, non-stationarity, i.e. non-constant mean, or/and non-constant variance, and/or covariance that is not solely the function of elapsed time between responses over the period of study, is another issue in the longitudinal study. It has been found that ignoring such departures may arise bias and provide misleading conclusions. As a remedy, negative binomial (NB) regression was suggested by the researcher for modelling longitudinal count. For longitudinal non-stationary count with over-dispersion, there is no established observation-driven model in the literature. Although there exists a non-stationary NB type model in the time series context, this type of observation-driven model has never been used in longitudinal data. In this paper, we have extended the non-stationary model to the longitudinal set-up and proposed a GQL estimation procedure for estimating regression parameters. An extensive simulation study has been carried out through which it has been shown that GQL provides unbiased estimates of the regression parameters. Performance of the method of moment approach for estimating correlation and over-dispersion parameter has also found to be consistent. The proposed model and estimation technique, thereafter, was applied to analyse longitudinal epileptic seizure count data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation problem for the semiparametric regression model with censored data in which the number of explanatory variables p in the linear part is much larger than sample size n, often denoted as p n. The purpose of this paper is to study the effects of covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. It should be noted that high variance and over-fitting are a major concern in such problems. Ordinary statistical methods for estimation cannot be applied directly to censored and high-dimensional data, and therefore a transformation is required. In the context of this paper, a synthetic data transformation is used for solving the censoring problem. We then apply the LASSO-type double-penalized least squares (DPLS) to achieve sparsity in the parametric component and use smoothing splines to estimate the nonparametric component. A Monte Carlo simulation study is performed to show the performance of the estimators and to analyse the effects of the different censoring levels. A real high-dimensional censored data example is used to illustrate the ideas discussed herein. [ABSTRACT FROM AUTHOR]

This paper proposes a modified adaptive lasso method by the Bayesian bootstrap (BBAL) and approximates the posterior distributions of parameters for a linear and a logistic regression model, respectively. The BBAL estimators are proved to have asymptotic and Oracle properties and they are acquired by the coordinate descent algorithm which could get the solutions at the grid of values of the penalty parameter λ. Three numerical experiments are conducted to demonstrate the BBAL method. Test results show the consistency of the variable selection and result in more robust estimators. And we use the median coefficients of the BBAL estimators to do the prediction with a medical dataset. [ABSTRACT FROM AUTHOR]

The semiparametric partial linear models are often used in real data analysis for its flexibility and parsimony. Statistical inference of this model is restricted with two conditions: (i) the linear and nonlinear parts are known in advance, (ii) the errors are independent. However, in practice, this is unreasonable to artificially determine which subset of variables have linear effect on the response and which have nonlinear effect. In addition, the assumption of errors being independent may be incorrect for time series data. Therefore, it is of great interest to develop some efficient methods to distinguish linear components from nonlinear ones with correlated errors. In this paper, we develop a method for identifying linear and nonlinear components, and estimate the coefficients of error structure. The performance of the proposed method is examined by simulation study and analyses a real data set for an illustration. [ABSTRACT FROM AUTHOR]

The statistical regression technique is an essential data fitting tool to explore the generation mechanism of the random phenomenon. Therefore, the model selection technique is becoming important. Meanwhile, bootstrap-based sample augmentation mechanisms are becoming indispensable when the reliable statistical inference of the model selection is expected to be made when the sample size is unsufficient. In this paper, the model selection performance of the bootstrap-based model selection criteria on the Tobit regression model are compared through the intensive Monte Carlo simulation experimentation. The simulation experiment demonstrates that the model identification risk of the recommended bootstrap-based model selection criteria can be adequately compensated by increasing the scientific computation cost in terms of the different bootstrap sample augmentation mechanisms. The recommended bootstrap-based model selection criterion is applied to fit the fidelity dataset. [ABSTRACT FROM AUTHOR]

A common assumption in non-parametric regression models is the independence of the covariate and the error. Some procedures have been suggested for testing that hypothesis. This paper considers a test, whose test statistic compares estimators of the joint and the product of the marginal characteristic functions of the covariate and the error. It is proposed to approximate the null distribution of such statistic by means of a weighted bootstrap estimator. The resulting test is able to detect any fixed alternative as well as local alternatives converging to the null at the rate n − 1 / 2 , n denoting the sample size. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared with other estimators. This study reveals that, from a computational point of view, the proposed approximation is very efficient. Two real data set applications are also included. [ABSTRACT FROM AUTHOR]

Multicollinearity is often ignored in censored regression model. In this respect, Tobit Liu estimation is proposed as an alternative in order to dispel the adverse effects of multicollinearity on the maximum likelihood estimation. Tobit Liu estimator is compared with Tobit ridge estimator and Tobit maximum likelihood estimator, theoretically via mean square error. For empirical analysis, we prefer Mroz dataset which is a phenomenon in the context of censored regression. Since many studies have investigated Mroz dataset by neglecting multicollinearity, we handle this dataset in the context of multicollinearity in this paper. Moreover, it is seen that multicollinearity is not included in pioneer studies' simulation designs. Therefore, we conduct a Monte Carlo simulation study where we take account of different levels of multicollinearity while generating data. Briefly, this study contributes to filling an important gap in the literature and proposes to investigate other econometrically censored data in the context of multicollinearity. [ABSTRACT FROM AUTHOR]

Varying-coefficient regression is a popular statistical tool that models the way a certain variable modulates the effect of other predictors nonlinearly. However, a majority of the VC regression models consider univariate responses; the case of multivariate responses have received relatively lesser attention. In this paper, we propose a robust multivariate varying-coefficient model based on rank loss that models the relationships among different responses via reduced-rank regression and penalized variable selection. Some asymptotic results are also established for the proposed methods. Using synthetic data, we investigate the finite sample performance and robustness properties of the estimator. We also illustrate our methodology by application to a real dataset on periodontal disease. [ABSTRACT FROM AUTHOR]

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of observations, must be solved prior to model fitting. This is also the case for regression models involving circular variables (supported on the unit circumference). In that context, using kernel regression methods, this paper provides a flexible alternative for constructing pilot estimators that allow to construct suitable statistics to perform no-effect tests and tests for equality and parallelism of regression curves. Finite sample performance of the proposed methods is analysed in a simulation study and illustrated with real data examples. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for the continuous response variable of interest, whereas the Bernoulli distribution is used for the point mass of the censoring observations. We estimate the corresponding parameters with the maximum likelihood method. Numerical evaluation of the model is performed by means of Monte Carlo simulations and of an illustration with real data. The results show the good performance of the proposed model, making it an addition to the tool-kit of biometricians, medical doctors, applied statisticians, and data scientists. [ABSTRACT FROM AUTHOR]

This paper proposes a novel estimation of coefficients in single-index regression models. Unlike the traditional average derivative estimation [Powell JL, Stock JH, Stoker TM. Semiparametric estimation of index coefficients. Econometrica. 1989;57(6):1403-1430; Hardle W, Thomas M. Investigating smooth multiple regression by the method of average derivatives. J Amer Statist Assoc. 1989;84(408):986-995] and semiparametric least squares estimation [Ichimura H. Semiparametric least squares (sls) and weighted sls estimation of singleindex models. J Econometrics. 1993;58(1):71-120; Hardle W, Hall P, Ichimura H. Optimal smoothing in single-index models. Ann Statist. 1993;21(1):157-178], the procedure developed in this paper is to estimate the coefficients directly by minimizing the mean variation function and does not involve estimating the link function nonparametrically. As a result, it avoids the selection of the bandwidth or the number of knots, and its implementation is more robust and easier. The resultant estimator is shown to be consistent. Numerical results and real data analysis also show that the proposed procedure is more applicable against model free assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we study the identification of Bayesian regression models, when an ordinal covariate is subject to unidirectional misclassification. Xia and Gustafson [Bayesian regression models adjusting for unidirectional covariate misclassification. Can J Stat. 2016;44(2):198–218] obtained model identifiability for non-binary regression models, when there is a binary covariate subject to unidirectional misclassification. In the current paper, we establish the moment identifiability of regression models for misclassified ordinal covariates with more than two categories, based on forms of observable moments. Computational studies are conducted that confirm the theoretical results. We apply the method to two datasets, one from the Medical Expenditure Panel Survey (MEPS), and the other from Translational Research Investigating Underlying Disparities in Acute Myocardial infarction Patients Health Status (TRIUMPH). [ABSTRACT FROM PUBLISHER]

In this paper we propose an alternative procedure for estimating the parameters of the beta regression model. This alternative estimation procedure is based on the EM-algorithm. For this, we took advantage of the stochastic representation of the beta random variable through ratio of independent gamma random variables. We present a complete approach based on the EM-algorithm. More specifically, this approach includes point and interval estimations and diagnostic tools for detecting outlying observations. As it will be illustrated in this paper, the EM-algorithm approach provides a better estimation of the precision parameter when compared to the direct maximum likelihood (ML) approach. We present the results of Monte Carlo simulations to compare EM-algorithm and direct ML. Finally, two empirical examples illustrate the full EM-algorithm approach for the beta regression model. This paper contains a Supplementary Material. [ABSTRACT FROM AUTHOR]

In this paper, we study the effects of near-singularity which is known as multicollinearity in the binary logistic regression. Furthermore, we also assume the presence of stochastic non-sample linear restrictions. The well-known logistic Liu estimator is combined with the stochastic linear restrictions in order to propose a new method, namely, the stochastic restricted Liu estimation. Theoretical comparisons between the usual maximum likelihood estimator, Liu estimator, stochastic restricted maximum-likelihood estimator and the new stochastic restricted Liu estimator are derived using matrix mean-squared errors of the estimators. A Monte Carlo simulation experiment is designed to evaluate the performances of the listed estimators in terms of mean-squared error and mean absolute error criteria. Artificial data are used to show how to interpret the theorems. According to the results of the simulation, the new method beats the other estimators when the data matrix has the problem of collinearity along with the stochastic restrictions. [ABSTRACT FROM AUTHOR]

Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean–covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well. [ABSTRACT FROM AUTHOR]

This paper proposes a data transformation to deal with the presence of constant under/over-dispersion relative to the Poisson or binomial assumptions. The proposed methodology is very simple as it does not require to replace the Poisson or binomial by more complex regression models based on more flexible distributions. The new approach consist of a transformation of the response variable, followed by the analysis of its relation with the covariates by applying to the transformed variable the usual Poisson or binomial regression models. The transformation depends on a tuning parameter, which can be easily chosen using a straightforward criterion. The efectiveness of the proposed approach is illustrated by simulation experiments and by analyzing six real data sets. [ABSTRACT FROM AUTHOR]

In this paper, a heteroscedastic functional regression model with martingale difference errors is considered. We are interested in real-time estimation of the regression as well as the conditional variance operators when the response is a real-valued random variable and the covariate belongs to an infinite-dimensional space. A Robbins–Monro-type estimator of the conditional variance is introduced when a sample is collected from an underlying stationary and ergodic process. First, a local uniform L q -consistency (for q ≥ 2) rate of the recursive estimator of the regression operator is established. Then, a pointwise mean-square consistency rate of the conditional variance is given when the regression function is supposed to be known and when it is estimated recursively. Simulation studies are conducted to assess the proposed estimator's performance, in terms of reducing the computational time without affecting significantly the accuracy, compared to its natural competitor. An application to real environmental data is also carried out to illustrate the real-time on day ahead prediction of the maximum ozone concentration in Mexico city as well as its volatility. [ABSTRACT FROM AUTHOR]

Extreme-value theory is useful for modelling extremal events. The behaviour of such extremal events may be impacted by other variables and such dependence is captured using a regression framework. In this paper, we develop residual based diagnostic analysis, generalized leverage, generalized Cook's distance and also global and local influence analysis for the generalized extreme-value nonlinear regression model. Two residuals for use with the model are proposed: the standardized and deviance residuals. Additionally, we present a model misspecification test that can be used to determine whether the fitted model is incorrectly specified. We also show how to perform nonnested testing inferences. Empirical applications based on simulated and observed data are presented and discussed. [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]

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

In this paper, we use the idea of order statistics from independent and non-identically distributed random variables to propose ordered partially ordered judgment subset sampling (OPOJSS) and then develop optimal linear parametric inferences. The best linear unbiased and invariant estimators of the location and scale parameters of a location-scale family are developed based on OPOJSS. It is shown that, despite the presence or absence of ranking errors, the proposed estimators with OPOJSS are uniformly better than the existing estimators with simple random sampling (SRS), ranked set sampling (RSS), ordered RSS (ORSS) and partially ordered judgment subset sampling (POJSS). Moreover, we also derive the best linear unbiased estimators (BLUEs) of the unknown parameters of the simple linear regression model with replicated observations using POJSS and OPOJSS. It is found that the BLUEs with OPOJSS are more precise than the BLUEs based on SRS, RSS, ORSS and POJSS. [ABSTRACT FROM AUTHOR]