Some Research Of Nonparametric Functional Data

For more than a decade,with abundant applications and emergence of functional data such as meteorological data and economic index,functional data analysis has been a hot topic in statistics.In fact,compared with the method of parametric regression which makes many assumptions on the model,the method of nonparameter regression depends on data completely,and it has strong adaptability and robustness,especially for nonlinear or nonhomogeneous problems.This fact is true for functional data analysis.In this dissertation,the method of nonparametric is employed to consider the statistical inference of conditional density function for the functional data,the main content is listed as follows:Firstly,we establish the joint asymptotic normality of the local linear estimation of the conditional density and its derivative for strong mixing dependent and functional data,by employing the method which is used to prove the joint asymptotic normality of the local linear estimation of the conditional density and its derivative for finite dimensional data.In addition,we verify the asymptotic normality via simulation.Secondly,we construct the confidence interval of the conditional density functi-on by using the empirical likelihood method for strong mixing dependent and functional data.Under some conditions,we establish that the empirical likelihood ratio statistic has an asymptotic standard chi-squared distribution with one degree of freedom.Thirdly,we propose the local linear estimation of conditional hazard rate for the independent functional data,and obtain the mean square convergence and asymptotic normality.The simulation results show that the empirical mean square errors of local linear estimation are smaller than those of kernel estimation.