The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing

Abstract

Abstract In this paper, considering the nonparametric regression model Y n i = g ( t i ) + ε i $Y_{ni}=g(t_{i})+\varepsilon_{i}$ ( 1 ≤ i ≤ n $1\leq i\leq n$ ), where ε i = ∑ j = − ∞ ∞ a j e i − j $\varepsilon_{i}=\sum_{j=-\infty}^{\infty}a_{j}e_{i-j}$ and e i − j $e_{i-j}$ are identically distributed and ρ-mixing sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of g ( ⋅ ) $g(\cdot)$ , the rates of the normal approximation are shown as O ( n − 1 / 6 ) $O(n^{-1/6})$ under certain conditions.

Keywords

• wavelet estimator
• ρ-mixing
• Berry-Esseen bound
• linear process