Strong consistency rates of estimators in semi-parametric errors-in-variables model with missing responses

Abstract

In this article, we focus on the semi-parametric error-in-variables model with missing
responses: yi = »i¯+g(ti)+²i, xi = »i+¹i, where yi are the response variables missing at random,
(»i; ti) are design points, »i are the potential variables observed with measurement errors ¹i, the
unknown slope parameter ¯ and nonparametric component g(¢) need to be estimate. Here we
choose three di®erent approaches to estimate ¯ and g(¢). Under appropriate conditions, we
study the strong consistency rates for the proposed estimators. In general, we concluded that
the strong consistency rates for all estimators can achieve o(n¡1=4).