Stochastic Restricted Estimator Research Articles

Ridge estimation in linear mixed measurement error models with stochastic linear mixed restrictions

This article is concentrated on the problem of multicollinearity in linear mixed models (LMMs) with measurement error in the fixed effects variables. After introducing a ridge estimator (RE) in these models, we propose a new estimator called the stochastic restricted ridge estimator (SRRE) by combining the ridge estimator (RE) and the stochastic restricted estimator (SRE). Moreover, asymptotic properties of these estimators will be derived and the necessary and sufficient conditions for the superiority of the SRRE over the RE and SRE are obtained using the mean squared error matrix (MSEM). Finally, the theoretical findings of the proposed estimators are also evaluated with a Monte Carlo simulation study and a numerical example.

Stochastic restricted Liu estimator in linear mixed measurement error models

This paper is concerned with the Liu estimator, stochastic restricted estimator and stochastic restricted Liu estimator of fixed and random effects in the linear mixed measurement error models. We compare the proposed estimators under the criterion of mean squared error matrix (MSEM). Furthermore, the selection of the Liu biasing parameter is discussed. A real data analysis is provided to illustrate the theoretical results and a simulation study is conducted to characterize the performance of estimators in the linear mixed measurement error model.

Stochastic Restricted Liu Type estimator for SUR model

In this paper, we introduce new Stochastic Restricted Estimator for SUR model, defined by Stochastic Restricted Liu Type SUR estimator (SRLTSE) . The propose estimator has deal with multicollinearity in SUR model if there is a degree of uncertainty in the parameters restriction. Moreover, the superiority of (SRLTSE) estimator was derived with respect to mean squared error matrix (MSEM) criteria. Finally, a simulation study was conducted. This simulation used standard mean squares error (MSE) criterion to illustrate the advantage between Stochastic Restricted SUR estimator (SRSE), Stochastic Restricted Ridge SUR estimator (SRRSE), and Stochastic Restricted Liu Type SUR estimator (SRLTSE) at several factors.Â

Stochastic Restricted Estimation in Partially Linear Measurement Error Models

As a generalization of nonparametric regression model, partially linear model has been studied extensively in the last decades. This paper considers estimation of the semiparametric model under the situation that the covariates are measured with additive error in the linear part and some additional stochastic linear restrictions exist on the parametric component. Based on the corrected profile least-squares approach and mixed regression method, we propose a stochastic restricted estimator named the corrected profile mixed estimator for the parametric component, and discuss its statistical properties. We also construct a weighted stochastic restricted estimation for the parametric component. Finally, the proposed procedure is illustrated by simulation studies.

Generalized preliminary test stochastic restricted estimator in the linear regression model

ABSTRACTIn this paper, we propose three generalized estimators, namely, generalized unrestricted estimator (GURE), generalized stochastic restricted estimator (GSRE), and generalized preliminary test stochastic restricted estimator (GPTSRE). The GURE can be used to represent the ridge estimator, almost unbiased ridge estimator (AURE), Liu estimator, and almost unbiased Liu estimator. When stochastic restrictions are available in addition to the sample information, the GSRE can be used to represent stochastic mixed ridge estimator, stochastic restricted Liu estimator, stochastic restricted almost unbiased ridge estimator, and stochastic restricted almost unbiased Liu estimator. The GPTSRE can be used to represent the preliminary test estimators based on mixed estimator. Using the GPTSRE, the properties of three other preliminary test estimators, namely preliminary test stochastic mixed ridge estimator, preliminary test stochastic restricted almost unbiased Liu estimator, and preliminary test stochastic restricted almost unbiased ridge estimator can also be discussed. The mean square error matrix criterion is used to obtain the superiority conditions to compare the estimators based on GPTSRE with some biased estimators for the two cases for which the stochastic restrictions are correct, and are not correct. Finally, a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings of the proposed estimators.

The generalized preliminary test estimator when different sets of stochastic restrictions are available

Arumairajan and Wijekoon (Commun Stat—Theor Methods, in press, 2014) proposed a generalized preliminary test stochastic restricted estimator (GPTSRE) to represent the preliminary test estimators when stochastic restrictions are available in addition to sample model. The aim of this paper is to define the GPTSRE when two different sets of competing stochastic restrictions are available. Moreover the conditions for superiority of GPTSRE based on one stochastic restriction over the other are derived with respect to mean square error (MSE) matrix criterion. Furthermore the estimator GPTSRE is theoretically compared with almost unbiased ridge estimator and almost unbiased Liu estimator in the MSE matrix sense. Finally a Monte Carlo simulation study and numerical example are done to illustrate the theoretical findings.

A Generalized Stochastic Restricted Ridge Regression Estimator

In this article, we introduce a new stochastic restricted estimator for the unknown vector parameter in the linear regression model when stochastic linear restrictions on the parameters hold. We show that the new estimator is a generalization of the ordinary mixed estimator (OME), Liu estimator (LE), ordinary ridge estimator (ORR), (k-d) class estimator, stochastic restricted Liu estimator (SRLE), and stochastic restricted ridge estimator (SRRE). Performance of the new estimator in comparison to other estimators in terms of the mean squares error matrix (MMSE) is examined. Numerical example from literature have been given to illustrate the results.