Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors

ABSTRACT

For the heteroscedastic regression model $Y_i=x_i\beta +g\left(t_i\right)+{\sigma }_i{e}_i,1\le i\le n$, where ${\sigma }_i^2=f\left(u_i\right)$, $(x_i,t_i,u_i)$ are known to be nonrandom design points, $g(\cdot )$ and $f(\cdot )$ are defined on the closed interval [0,1]. When $f(\cdot )$ is known, we investigate the Berry–Esseen type bounds for wavelet estimators of β and $g(\cdot )$ under $\left\{e_i\right\}$ are identically distributed ϕ-mixing random errors, when $f(\cdot )$ is unknown, the Berry–Esseen type bounds for wavelet estimators of β, $g(\cdot )$ and $f(\cdot )$ established under $\left\{e_i\right\}$ are independent random errors.

Keywords:

• Berry–Esseen bound
• heteroscedastic regression model
• wavelet estimator
• ϕ-mixing
• random errors

2010 AMS SUBJECT CLASSIFICATIONS:

• 62F12
• 60F15

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [11271189,11461057], National Science Foundation of Jiangxi Province [20161BAB201003], 2017 youth teacher research and development fund project of Guangxi University of Finance and Economics [2017QNA01].