The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors

Abstract

Consider the nonparametric regression model Yni = g(tni) + εi, i = 1, 2, …, n, n ≥ 1, where εi, 1 ≤ i ≤ n, are asymptotically negatively associated (ANA, for short) random variables. Under some appropriate conditions, the Berry-Esseen bound of the wavelet estimator of g(⋅) is established. In addition, some numerical simulations are provided in this paper. The results obtained in this paper generalize some corresponding ones in the literature.

Asymptotic Properties of Conditional Value-at-risk Estimate for Asymptotic Negatively Associated Samples

“…Yuan and Wu [17] delved into the limiting behavior of the maximum of partial sums under residual Cesaro alpha-integrability assumptions. Tang et al [18] established a Berry-Esseen type bound for wavelet estimators in a nonparametric regression model with ANA errors. Wu et al [19] established a general result on complete moment convergence and the Marcinkiewicz?CZygmund-type strong law of large numbers for weighted sums of masymptotic negatively associated random variables.…”