Asymptotic Optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors

This paper proposes the Nonnegative Garrote(NG)estimator for linear model with heteroscedastic errors.On the other hand,under some regularity conditions,the authors show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model average estimator.Simulation results and a real data analysis are reported for testing the results obtained previously.These results provide a stronger theoretical basis for the use of NG estimator by strengthening existing findings.

Linear regression under model uncertainty

We reexamine the classical linear regression model when it is subject to two types of uncertainty:(i)some covariates are either missing or completely inaccessible,and(ii)the variance of the measurement error is undetermined and changing according to a mechanism unknown to the statistician.By following the recent theory of sublinear expectation,we propose to characterize such mean and variance uncertainty in the response variable by two specific nonlinear random variables,which encompass an infinite family of probability distributions for the response variable in the sense of(linear)classical probability theory.The approach enables a family of estimators under various loss functions for the regression parameter and the parameters related to model uncertainty.The consistency of the estimators is established under mild conditions in the data generation process.Three applications are introduced to assess the quality of the approach including a forecasting model for the S&P Index.

Jackknifed Liu Estimator in Linear Regression Models

In this paper, we introduce a generalized Liu estimator and jackknifed Liu estimator in a linear regression model with correlated or heteroscedastic errors. Therefore, we extend the Liu estimator. Under the mean square error（MSE）, the jackknifed estimator is superior to the Liu estimator and the jackknifed ridge estimator. We also give a method to select the biasing parameter for d. Furthermore, a numerical example is given to illustvate these theoretical results.

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.