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

In this article, we focus on the semi-parametric error-in-variables model with missing responses: yi = ξiβ + 1(ti) + i, xi = ξi + μi, where yi are the response variables missing at random, (ξi, ti) are design points, ξi are the potential variables observed with measurement errors μi, the unknown slope parameter β and nonparametric component 1(·) need to be estimate. Here we choose three different approaches to estimate β and 1(·). 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).