Abstract
ABSTRACTIn 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.
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