On The Research Of Some Problems Of The Wavelet Estimation For Semiparametric Regression Model

In this thesis, We considers an important semiparametric regression model. y_i = x_iβ+ g (t_i ) + ei,1≤i≤n. Where x i∈R1 ,t_i∈[0,1],{( x_i , t_i),1≤i≤n}are the fixed design points,βis an unkown parameter to be estimated, g ( t ) is an unkown Borel function which defined on [ 0,1] , {e_i ,1≤i≤n}are random errors with Ee_i = 0, Ee_i~2 =σ~2, i = 1,2 , n. We uses the least square estimate combining with the wavelet method and defines the estimators (β|^)_n, (g|^)_n(t )forβ, g ( t ).When the errors areα-mix_ing sequences, we get the strong consistency of the estimator. When the errors areρ|~-mix_ing and NA sequences,we get the strong consistency of the estimator and the r-th mean consistency of the estimator,the corresponding research results in the ex_istig literature have been expanded.