设回归模型Y(ni)=g(t(ni))+ε(ni),i=1,…,n,其中{t(ni)}为固定设计点列,g(·)是定义在[0,1]上的未知函数,{ε(ni)}为随机误差.该文主要讨论了误差为强混合序列情形下,回归函数g(·)小波估计的Berry-Esseen界,其界可达O(n^(-1/6)).
Consider the nonparametric regression model Y(ni)=g(t(ni)) +ε(ni)(i = 1,...,n) with wavelet method,where the design points {t(ni)} are known and nonrandom,g(.) is an unknown function defined on the closed interval[0,1],and {ε(ni)} are strictly stationary strong mixing processes.Under appropriate conditions,we derive Berry-Esseen bounds for wavelet estimator of g(.).As a corollary,we give the Berry-Esseen bounds that can attain O(n^(-1/6)).