弱相依半参数回归模型的加权小波估计的渐近正态性

ASYMPTOTIC NORMALITY OF WEIGHTED WAVELET ESTIMATORS IN A SEMIPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT ERRORS

本文研究了半参数回归模型y_i=X'_iβ+g(t_i)+e_i,i=1,2,···,n,其中{e_i}为ψ-弱相依随机误差序列.利用小波估计的方法得到了参数、非参数的加权小波估计量.在相当一般的条件下,获得了这些小波估计量的渐近正态性,不仅推广了半参数回归模型的相应结果,而且在一定程度上统一了相依半参数回归模型的渐近正态性的理论.

Consider the following semiparametric regression model yi= X＇iβ ＋ g（ti） ＋ ei, i =1, 2, · · ·, n, where random errors {ei} are ψ-weakly dependent. Using the wavelet method, we obtain some estimators of the parametric component and the nonparametric component. Under general conditions, we investigate the asymptotic normality of these wavelet estimators. We not only generalize the corresponding conclusions of semiparametric regression models, but also unify asymptotic normal theorey of semiparametric regression models with dependent errors to some certain degree.