Restricted estimation and testing of hypothesis in linear measurement errors models

ABSTRACT

In this article, the linear models with measurement error both in the response and in the covariates are considered. Following Shalabh et al. (2007, 2009), we propose several restricted estimators for the regression coefficients. The consistency and asymptotic normality of the restricted estimators are established. Furthermore, we also discuss the superiority of the restricted estimators to unrestricted estimators under Pitman closeness criterion. We also develop several variance estimators and establish their asymptotic distributions. Wald-type statistics are constructed for testing the linear restrictions. Finally, Monte Carlo simulations are conducted to illustrate the finite-sample properties of the proposed estimators.

Keywords:

• Linear restrictions
• Measurement errors
• Pitman closeness
• Wald type statistic

Mathematics Subject Classification:

• 62J05
• 62F10
• 62F03

Acknowledgments

The authors sincerely thank the editor and the referees for their helpful and constructive comments which led to an improved version of the original paper.

Funding

Wenxue Li's research was supported by the Doctoral Starting up Foundation of Jiangxi University of Science and Technology, China (jxxjbs12002) and Research Fund of Jiangxi University of Science and Technology (NSFJ2015-K17). Hu Yang’s research was supported by the National Natural Science Foundation of China (11171361). Tingting Li’s research was partially supported by the National Natural Science Foundation of China(11201505), the Fundamental Research Funds for the Central Universities (XDJK2013C021) and the Southewest University doctoral grant (SWU113012).