Asymptotic Properties for Estimators in a Semiparametric EV Model with NA Errors and Missing Responses.

This article deals with the semiparametric errors-in-variables (EV) model y i = ξ i β + g t i + ϵ i , x i = ξ i + μ i , where y i are the random missing response variables, ξ i , t i are the design points, ξ i are the potential variables observed with measurement errors μ i , and random errors ϵ i are negatively associated (NA) variables. In addition, we need to estimate the unknown slope parameter β and nonparametric component g · . In order to solve the missing responses, we introduce three different approaches to get the estimators of β and g · . Meanwhile, we study the asymptotic properties for all the estimators. The final results show that the strong consistent rates for all the estimators can achieve o n − 1 / 4 . The asymptotic normality for all the estimators is considered. We compare the finite sample performance of the three estimators by simulation as well. [ABSTRACT FROM AUTHOR]