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.

Keywords:

• Asymptotic normality
• heteroscedastic semiparametric regression model
• wavelet estimator
• ϕ-mixing

2010 AMS Subject Classifications:

• 62F12
• 60F15

Acknowledgements

The authors are grateful to the editor and the referees for their thoughtful and constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11271189], Liwang Ding's research was partially supported by the Natural Science Foundation of Guangxi [grant number 2020GXNSFBA159045].