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Estimation and prediction of regression models with partition forms are widely applied techniques in statistical inference and data analysis. In this paper, we consider some fundamental inference problems regarding a linear random-effects model (LREM) and its reduced models without statistical distribution assumptions for error terms. We shall present a partition form of LREM and its correctly-reduced models, introduce the consistency concepts of the LREM and its reduced models, define the predictability/estimability of unknown parameters in the LREM and its reduced models, establish the matrix equations and analytical formulas associated with best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) of all unknown parameter vectors in the LREM and its reduced models, and present many fundamental decomposition equalities for the BLUPs/BLUEs of all unknown parameters in the LREM and its reduced models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a variable selection method for quantile regression model in ultra-high dimensional longitudinal data called as the weighted adaptive robust lasso (WAR-Lasso) which is double-robustness. We derive the consistency and the model selection oracle property of WAR-Lasso. Simulation studies show the double-robustness of WAR-Lasso in both cases of heavy-tailed distribution of the errors and the heavy contaminations of the covariates. WAR-Lasso outperform other methods such as SCAD and etc. A real data analysis is carried out. It shows that WAR-Lasso tends to select fewer variables and the estimated coefficients are in line with economic significance. [ABSTRACT FROM AUTHOR]

This paper studies a linear regression model with asymptotically almost negatively associated (AANA, in short) random errors. Under some mild conditions, the weak consistency of M-estimator of the unknown parameter is investigated, which extend the corresponding results for independent random errors and negatively associated (NA, in short) random errors. At last, two simulation examples are presented to verify the weak consistency of M-estimator in the model. [ABSTRACT FROM AUTHOR]

Parametric regression models with certain parameter restrictions occur widely in statistical data analysis and inference. In some cases, we may wish to impose linear constraints on some subsets of fixed parameters in a given parametric regression model. This paper is concerned with some fundamental inference problems on a general linear model y = X β + ε in which the unknown parameter vector β is subject to a linear matrix equation restriction A β = b . We shall introduce the technical concepts and definitions of consistency, predictability, estimability, and formulas of the best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) under a constrained general linear model (CGLM). We then show how to establish BLUPs/BLUEs of all unknown parameters in the CGLM, and present various properties of the BLUPs/BLUEs using the methodology of matrix ranks and inertias. [ABSTRACT FROM AUTHOR]

In this note, we make some comments about the paper of Alheety and Kibria (2014) and correct the wrongly proved Theorems in that paper. [ABSTRACT FROM AUTHOR]

This paper shows the importance of the use of Monte Carlo experiments within Simple Linear Regression (SLR) Models through Refined Descriptive Sampling and proves practically that the asymptotic theory of the Ordinary Least Squares (OLS) estimator still hold with small samples when the Normality errors assumption is released. To this end, a simple Linear Regression adaptive Refined Descriptive Sampling (L2RDS) algorithm is proposed to estimate the parameter of SLR models by OLS method and computes its properties. Real data are used to properly specified the simulation model. The results show that L2RDS algorithm provides accurate and efficient point estimates. [ABSTRACT FROM AUTHOR]

In this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of estimators called the stochastic restricted almost unbiased ridge-type principal component estimator (SRAURPCE) and the stochastic restricted almost unbiased Liu-type principal component estimator (SRAURPCE) to overcome the well-known multicollinearity problem in linear regression model. For the two cases when the restrictions are true and not true, necessary and sufficient conditions for the superiority of the proposed estimators are derived and compared, respectively. Furthermore, a Monte Carlo simulation study and a numerical example are given to illustrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, the preliminary test approach to the estimation of the linear regression model with student'sterrors is considered. The preliminary test almost unbiased two-parameter estimator is proposed, when it is suspected that the regression parameter may be restricted to a constraint. The quadratic biases and quadratic risks of the proposed estimators are derived and compared under both null and alternative hypotheses. The conditions of superiority of the proposed estimators for departure parameter and biasing parameterskanddare derived, respectively. Furthermore, a real data example and a Monte Carlo simulation study are provided to illustrate some of the theoretical results. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models. [ABSTRACT FROM AUTHOR]

In this paper, we present a multivariate version of the skewed log-Birnbaum–Saunders regression model. This new family of distributions holds good properties such as marginal variables following univariate skewed log-Birnbaum–Saunders distributions, besides presenting the usual log-Birnbaum–Saunders distribution as a particular case. Furthermore, the model parameters are estimated through maximum-likelihood methods, a closed-form expression for the Fisher’s information matrix is presented, and testing hypothesis for model parameters is performed. Two real datasets are analyzed and results are discussed. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariatet-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modified maximum likelihood estimation method that provides the estimator, called modified maximum likelihood estimator (MMLE), in closed form. These estimators are shown to be unbiased, efficient, and robust as compared to the widely used least square estimators (LSEs). Also, the tests based upon MMLEs are found to be more powerful than the similar tests based upon LSEs. [ABSTRACT FROM PUBLISHER]

An outlier is defined as an observation that is significantly different from the others in its dataset. In high-dimensional regression analysis, datasets often contain a portion of outliers. It is important to identify and eliminate the outliers for fitting a model to a dataset. In this paper, a novel outlier detection method is proposed for high-dimensional regression problems. The leave-one-out idea is utilized to construct a novel outlier detection measure based on distance correlation, and then an outlier detection procedure is proposed. The proposed method enjoys several advantages. First, the outlier detection measure can be simply calculated, and the detection procedure works efficiently even for high-dimensional regression data. Moreover, it can deal with a general regression, which does not require specification of a linear regression model. Finally, simulation studies show that the proposed method behaves well for detecting outliers in high-dimensional regression model and performs better than some other competing methods. [ABSTRACT FROM AUTHOR]

In this paper, we translate variable selection for linear regression into multiple testing, and select significant variables according to testing result. New variable selection procedures are proposed based on the optimal discovery procedure (ODP) in multiple testing. Due to ODP’s optimality, if we guarantee the number of significant variables included, it will include less non significant variables than marginalp-value based methods. Consistency of our procedures is obtained in theory and simulation. Simulation results suggest that procedures based on multiple testing have improvement over procedures based on selection criteria, and our new procedures have better performance than marginalp-value based procedures. [ABSTRACT FROM AUTHOR]

In a mixture experiment, the response depends on the mixing proportions of the components present in the mixture. Optimum designs are available for the estimation of parameters of the models proposed in such situations. However, these designs are found to include the vertex points of the simplex Ξ defining the experimental region, which are not mixtures in the true sense. Recently, Mandal et al. (2015) derived optimum designs when the experiment is confined to an ellipsoidal region within Ξ, which does not include the vertices of Ξ. In this paper, an attempt has been made to find optimum designs when the experimental region is a simplex or is cuboidal inside Ξ and does not contain the extreme points. [ABSTRACT FROM PUBLISHER]

Multiple linear regression models are frequently used in predicting unknown values of the response variabley. In this case, a regression model's ability to produce an adequate prediction equation is of prime importance. This paper discusses the predictive performance of ther-kandr-dclass estimators compared to ordinary least squares (OLS), principal components, ridge regression and Liu estimators and between each other. The theoretical results are illustrated using Portland cement data and a region is established where ther-kand ther-dclass estimators are uniformly superior to the other mentioned estimators. [ABSTRACT FROM AUTHOR]

As direct generalization of the quantile regression for complete observed data, an estimation method for quantile regression models with interval censored data is proposed, and the property of consistency is obtained. The property of asymptotic normality is also established with a bias converging to zero, and to reduce the bias, two bias correction methods are proposed. Methods proposed in this paper do not require the censoring vectors to be identically distributed, and can be applied to models with various covariates. Simulation results show that the proposed methods work well. [ABSTRACT FROM AUTHOR]

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new restricted two-parameter (RTP) estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. We show that our new biased estimator is superior in the matrix mean square error criterion to the restricted ridge estimator proposed by Groß (2003), restricted Liu estimator introduced by Kaçiranlar et al. (1999), and RTP estimator introduced by Özkale and Kaçiranlar (2007). A numerical example and a Monte Carlo simulation have been analyzed to illustrate some of the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, we obtain an adjusted version of the likelihood ratio (LR) test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modifiedLRstatistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari (Advances in Statistical Analysis, 2010,94, pp. 75–87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standardLRtest. [ABSTRACT FROM PUBLISHER]

Building on the work of Lustbader and Moolgavkar (1985), this paper studies influence diagnostics for score tests. The diagnostic proposed by Lustbader and Moolgavkar is reassessed, and alternative diagnostics are proposed. The new diagnostics are based on one-step approximations to the change in the parameter estimates, resulting from deleting one observation. The use of the different diagnostics is illustrated with simulations and with an example. [ABSTRACT FROM AUTHOR]