ψ-混合异方差误差下半参数回归模型的加权小波估计

Weighted Wavelet Estimation in Semiparametric Regression Models with ψ-mixing Heteroscedastic Errors

考虑半参数回归模型y_i=x_iβ+g(t_i)+σ_ie_i,i=1,2,…,n其中(x_i,t_i,v_i)是固定设计点列,e,为ψ-混合随机误差.用小波估计方法得到了参数,非参数及误差方差的加权小波估计量.在相当一般的条件下,得到了这些小波估计量的渐近正态性及弱收敛速度.

Abstract Consider the following semiparametric regression model yi=xiβ＋g（ti）＋σiei,i=1,2,…,n, where （xi, ti, ui） are fixed design and random errors are C-Mixing. Using the wavelet method, we obtain some estimators of the parametric component, the nonparametric component and the variance function. Under general conditions, we investigate the asymptotic normality and weak consistence rates of these wavelet estimators.