Strong consistency rates for the estimators in a heteroscedastic EV model with missing responses

[摘要] This article is concerned with the semi-parametric error-in-variables (EV) model with missing responses: $y_{i}= \xi _{i}\beta +g(t_{i})+\epsilon _{i}$, $x_{i}= \xi _{i}+\mu _{i}$, where $\epsilon _{i}=\sigma _{i}e_{i}$ is heteroscedastic, $f(u_{i})=\sigma ^{2}_{i}$, $y_{i}$ are the response variables missing at random, the design points $(\xi _{i},t_{i},u_{i})$ are known and non-random, β is an unknown parameter, $g(\cdot )$ and $f(\cdot )$ are functions defined on closed interval $[0,1]$, and the $\xi _{i}$ are the potential variables observed with measurement errors $\mu _{i}$, $e_{i}$ are random errors. Under appropriate conditions, we study the strong consistent rates for the estimators of β, $g(\cdot )$ and $f(\cdot )$. Finite sample behavior of the estimators is investigated via simulations.

[学科分类] 电力

[关键词] Semi-parametric error-in-variables model;Heteroscedastic;Missing responses;Strong consistent rate