The asymptotic of the estimators in a semiparametric regression model under α -mixing errors

This is the authors' abstract. We don't add key points for this paper.

In this article, we consider the semiparametric regression model yi(n)=xi(n)β+g(ti(n))+εi(n), 1≤i≤n, where (xi(n),ti(n)) are the design points and εi(n) are α-mixing random variables. The unknown slope parameter β and non parametric component g(⋅) are estimated by the least-squares estimation and weight functions estimation. Under some suitable conditions, the r-th (r > 2) moment consistency, uniformly r-th (r > 2) moment consistency, complete consistency, and uniformly complete consistency for the estimators are presented under α-mixing errors. In addition, in order to demonstrate the validity of theoretical results, the finite sample behaviors of the estimators are considered via simulation study and real data analysis.