半参数回归的线性小波光滑

Wavelet Smoothing in Semiparametric Regression Model

摘要: 考虑半参数回归模型上未知函数，y_i=x_i^\prime \beta+g\left(t_i\right)+e_i, 1 \leq i \leq n,g(·)为R¹上未知参数,β∈R^p为待估参数Antoniads3中给出了非参数回归模型的小波估计，借鉴3我们利用偏残差法给出了β、g(·)的小波估计\widehat\beta, \widehatg(\cdot).本文研究了\widehat\beta, \widehatg(\cdot)的弱相合性及它们偏差和方差的渐近性质，并且得到了\widehat\beta的渐近正态性。

Abstract: Consider the semiparametric regression model gived by Y_i=x_i^\prime \beta+g\left(t_i\right)+e_i, \quad 1 \leq i \leq n.. Our goal is to estimate β and g(·) based on \left\Y_i, x_i, t_i\right\_i=1^n, we apply wavelet smoothing to the model and study the asymptotic behavior of tile wavelet estimators.