We investigate the heteroscedastic regression model Y_ni = g(x_ni) + σ_niε_ni, i = 1, . . . , n, where \( {\sigma}_{ni}^2 \) = f(u_ni), (x_ni, u_ni) are known fixed design points, g and f are unknown functions, and the errors ε_ni 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.

我们研究了异方差回归模型Ŷ _NI =克（X _NI）+ σ _NI ε _NI，我= 1 ，。。。中，n，其中\（{\西格玛} _ {NI} ^ 2 \） = ˚F（Ú _NI），（X _NI，U _NI）是已知的固定的设计点，克和˚F是未知的功能，且误差ε _NI假定形成一个平稳的α-混合随机变量。在某些温和条件下，我们获得f的小波估计的渐近正态性，证明它们的渐近正态性，并建立g的小波估计的Berry-Esseen型界。同样，在给定条件下，我们研究了g的估计量的Berry-Esseen型边界。对于任何δ> 0，它是顺序ø（N-（^{1 / 30）+ δ}）。最后，我们进行了全面的模拟研究，以证明所获得的理论结果的有效性。