Wavelet estimation in heteroscedastic regression models with alpha-mixing random errors

摘要

We investigate the heteroscedastic regression model Y-ni = g(x(ni)) + sigma(ni)epsilon(ni), i = 1, . . . , n, where sigma(2)(ni) = f(u(ni)), (x(ni), u(ni)) are known fixed design points, g and f are unknown functions, and the errors epsilon(ni) are assumed to form a stationary alpha-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 delta > 0, it is of order O(n-((1/30)+delta)). Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.