回归函数非线性小波估计的一致强相合性

Universal Strong Consistency of Nonlinear Wavelet Regression Estimation

摘要: 设(X₁, Y₁,…, （X_n,Y_n）是从总体（X, Y）中抽取的i.i.d.样本且服从0,1上的均匀分布．本文在平方积分损失下得到了回归函数g（x）= E（Y|X =x）的非线性小波估计的一致相合性。

Abstract: Let (X₁, Y₁,…, （X_n,Y_n） be i.i.d. samples from （X, Y） and X be uniform distributed on 0,1. In this paper, only asking the condition EY² ＜ ∞,no conditions on the distribution of Y and no smoothing conditions on the regression function g（x）= E（Y|X =x）, we get the strong consistency of nonlinear wavelet regression estimation under sqare integrated loss.