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

Abstract

This article deals with the semiparametric errors-in-variables (EV) model yi=ξiβ+gti+ϵi, xi=ξi+μi, where yi are the random missing response variables, ξi,ti are the design points, ξi are the potential variables observed with measurement errors μi, and random errors ϵi 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 on−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.