Asymptotic Properties Of Nonparametric Estimators For Fixed Design Models With Dependent Random Errors

Nonparametric regression is a hot topic in statistics.The commonly used methods in the estimation of regression function are wavelet estimation method,kernel estimation method and spline estimation method.When the error is independent,the research results are very rich.However,in practi-cal applications,the error generally does not satisfy the independent condi-tion.When the error is generalized to a dependent sequence,the study of the asymptotic properties of the regression function estimate is a problem worth exploring.The fixed design model is a nonparametric statistical model widely used in medical,biological,economic and other fields.In this paper,the asymptotic properties of nonparametric estimators of re-gression functions are discussed by using the methods of kernel estimation and wavelet estimation under the condition that the errors are different dependent sequences.Firstly,the asymptotic normality of wavelet estimators for fixed design model of a-mixed sequence is given.Secondly,discussed the uniform asymptotic normality of kernel estimators for fixed design model of the PA random variables sequence.Under suitable conditions to give the convergence speed obtained as O(n^-1/6)..Then,Under the linear process error of the LNQD sequence,The Berry-Esseen bound of wavelet estimation for fixed design mod-el is discussed.Under suitable conditions,the convergence rate obtained as O(n^-1/6).Finally,in the case of linear process error of ?-mixed sequence,the Berry-Esseed bound of kernel estimation for fixed design model is discussed.The convergence rate obtained as O(n^-1/6)under suitable conditions.