Error Is L ~ P-mixing Sequences And Weakly Stationary Linear Process Regression Model

This paper consists of two parts: In the first part, we will discuss the prob-lem of the pth-mean, complete consistency for the estimators of a nonparamet-ric and linear model with L~p-mixingale errors;In the second part, we will dis-cuss the problem of the rth-mean,complete consistency for the estimators of themodels above with weak stationary linear process errors and the uniformly mean consistency.To the nonparametric model Y_ni=g(x_ni)+ε_ni,1≤i≤n, Let g_n(x)=W_ni(x,W_n1,…?xnn)Y_ni estimate the unknown function g(x) .To the linear model y_i-x_i1β1+ …?+ x_iq?β_q, we use LSE β_nj to estimate the unknown parametric β_j.We mainly do the following works.In chapter Ⅱ . We study the models above with L_p-mixingale errors. We still obtain the pth-ean consistency for the estimators after omitting the uni-formly integrability of {|ε_n|β,n≥1} and {|ε_ri|β,1≤i≤n,n≥1} and the com-pletely consistency for the estimators which is a new result. Our results general-ize and improve the results in [4].In chapter Ⅲ , we study the nonparametric and linear model with weak sta-tionary linear model. To the nonparametric model, we still obtain the rth-mean and completely consistency which generalize and improve the results in [4]; To the linear model,we obtain the rth-mean and completely consistency which is a new result. These results generalize and improve the results in [1],[2],and [3].