2010•Shuxue de shijian yu renshiRequires access

Moment Consistency of Wavelet Estimation in Semiparametric Regression Models

Hongchang Hu

Abstract

Useing the wavelet method,consider the semiparametric regression model given by y_i=X_i~Tβ+g(t_i)+e_i(1≤i≤n) whereβis a d×1 unknown parametric vector,g(t) is an unknown Borel function on[0,1],X_i is a d×1 random design vector,random error{e_i} is martingale difference sequences,{t_i} is constant sequence on[0,1].In the paper,the q-order moments consistency of parametric and nonparametric wavelet estimators are studied.

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Key concepts: Mathematics, Semiparametric regression, Estimator, Martingale difference sequence, Wavelet, Strong consistency, Semiparametric model, Nonparametric regression