Statistical estimation for heteroscedastic semiparametric regression model with random errors

Abstract

This paper is concerned with the estimating problem of heteroscedastic semiparametric regression model. We investigate the asymptotic normality for wavelet estimators of the slope parameter and the nonparametric component in the case of known error variance with ϕ-mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.