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.

Profile Inferences on Restricted Additive Partially Linear EV Models

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

Statistical Inference for a Kind of Nonlinear Regression Model

As we all know, statistical inference of linear models has been a hot topic of statistical and econometric research. However, in many practical problems, the variable of interest and covariates are often nonlinear relationship. The performance of the statistical inference using linear models model can be very poor. In this paper, the statistical inference of a nonlinear regression model under some additional restricted conditions is investigated. The restricted estimator for the unknown parameter is proposed. Under some mild conditions, the asymptotic normality of the proposed estimator is established on the basis of Lagrange multiplier and hence can be used to construct the asymptotic confidence region of the regression parameter.