Nonparametric Recursive Regression M-estimation For Functional Stationary Ergodic Data

Nonparametric estimation,as a popular field of statistics,often faces the presence of outliers or residual heavy tails.Therefore,the M estimation method which can reduce the robustness of the estimation is of great research significance,and the related results are also concerned by the scholars.There are few data independence in the actual study,although mixing is the weakest of the common mixing conditions,it is difficult to verify whether the nonlinear time series meets the mixing conditions or not.Therefore,it is necessary to study the ergodic data that does not require many conditions to verify and can contain mixed structures that can not be included in all.In recent years,some scholars have established improved M estimation method,and the purpose is to estimate the original strengths of M as well as to absorb the advantages of other estimates.In this paper,the recursive M-estimation method is used to study the convergence rate and asymptotic properties of the nonparametric robust estimation of function data under the condition of smooth traversal.The main contents are as follows:1.The rate of convergence based on the robust ergodic functional non-parametric recursive M estimation On the basis of robust ergodic functional data,the thesis creates the recursive M estimation of functional non-parameter regression function.It uses some reasonable regularity conditions to prove that the non-parametric robust regression estimation value is almost exactly in uniform convergence with its non-parametric estimated natural estimation value,and adds the instance as validation,which has generalized the existing results in the literatures.2.The asymptotic distribution based on the robust ergodic functional non-parametric M estimation /recursive M estimation on the basis of robust ergodic functional data,the thesis adds some regular conditions,and obtains the asymptotic normality of nonparametric robust regression estimators and its natural estimated value from the nonparametric estimation through reasonable calculation and proof,which has generalized the related results in the existing literatures.