Variable Bandwidth Local Linear Estimation Of Nonparametric Regression Model And Its Statistical Properties

Nonparametric model is widely used in the practical problems,the reason is that the form of the regression function in the nonparametric model is free,and the limits to the random variate(X, Y) are fewer.In the past several decades ,this model is studied carefully by the researchers of statistics, and many achievements are arrived in both theorial fields and in applicational fields.In this paper ,we suppose that (X,Y) is RxRr.v. andE|Y| < (X1,Y1),(X2, Y2) …( Xn,Yn) are i.i.d samples from the population (X,Y). m(x) is a unkown un-variate function that satisfy:The research object of this paper is to estimate m(x) using the samples (X1, Y1),(X2, Y2), …?( Xn, Yn) , and to discuss the large sample properties.In this paper ,we give a kernel shape estimation of m(x) using variable bandwidth local linear refression approch, and discuss the asymptotic normality,the convergence rate of mean square and convergence rate with probability.The variable bandwidth local linear regression method we used in this paper have the advantages of both the local linear regression method and the variable bandwidth idea .the variable bandwidth henced the flexibility of the estimation .and it make this method can fit the spacial complex curve very well.and the asymptotic results of the estimation found the theoretic base for find the best variable bandwidth and drive the pratical best variable bandwidth from data directly.