Universal Strong Consistency of Nonlinear Wavelet Regression Estimation

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.