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

设（Ｘ_１，Ｘ_１），…，（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．

Let (X_1, Y_1,…, (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 EY^2 < ∞c 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.