Asymptotic normality of wavelet estimators in heteroscedastic regression model with ANA errors

Xufei Tang and Aiting Shen

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 14, 4283-4305

Abstract: In this article, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with asymptotically negatively associated (ANA or ρ−, for short) errors. Under some mild conditions, the asymptotic normality of the wavelet estimators of g(⋅) in the heteroscedastic regression model with ANA errors is obtained when f(⋅) is a known or unknown function, respectively. At the same time, we derive a Berry-Esseen-type bound for the estimators of g(⋅). As a corollary, by making a certain choice of the weights, the Berry-Esseen-type bound of the estimator can reach nearly O(n−1/12), which in some sense generalizes or improves the corresponding ones for negatively associated (NA, for short) random variables and φ−mixing sequence. Finally, the finite sample simulation study presented in this article shows the validity of our theoretical results.

Date: 2025
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DOI: 10.1080/03610926.2024.2417822

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