Wavelet estimation in heteroscedastic regression models with α-mixing random errors∗

Abstract

We investigate the heteroscedastic regression model Yni = g(xni) + σnieni, i = 1, . . . , n, where $$ {\sigma}_{ni}^2 $$ = f(uni), (xni, uni) are known fixed design points, g and f are unknown functions, and the errors eni are assumed to form a stationary α-mixing random variables. Under some mild conditions, we obtain the asymptotic normality for wavelet estimators of f, prove their the asymptotic normality, and establish the Berry–Esseen-type bound for wavelet estimators of g. Also, by the given conditions we study the Berry–Esseen-type bound for estimators of g; for any δ > 0, it is of order O(n−(1/30)+δ). Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.