Strong consistency rate of estimators in heteroscedastic errors-in-variables model for negative association samples

Abstract

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables (EV) models. We derive the strong consistency rate for estimators of the slope parameter and the nonparametric component in the case of known error variance with negative association (NA) random errors. Meanwhile, when the error variance is unknown, the strong consistency rate for the estimators of the slope parameter and the nonparametric component as well as variance function
are considered for NA samples. In general, we concluded that the strong consistency rate for all estimators can achieve $o(n^{-1/4})$.