固定设计下回归函数的小波估计

Nonparametric Wavelet Estimation of a Fixed Designed Regression Function

对于非参数回归模型 :Yi=g( ti) + εi,i=1 ,… ,n,其中 {ti}为固定设计点列 ,{εi}为 α-混合的平稳序列 ,该文建立了回归函数 g( t)的小波估计并研究了其相合性。

In this article the authors consider the nonparametric regression model:$Y-i=g(t-i)+ε-i,i=1,…,n$ where ${t-i}$ be a set of fixed designed points and $ {ε-i}$ be α-mixing stationary process. Here the authors adopt wavelet method to estimate g(t) and study its consistency, strong consistency and convergence rate.