K-nearest Neighbours Estimation Of Functional Nonparametric Regression Model For Dependent And Missing Sample

Functional data with dependent structures,such as functional time series data with? mixing structures,is an important problem in the field of functional data analysis(FDA).And the nonparametric regression model k nearest neighbor(KNN)estimation is always a powerful tool for processing functional data,and plays an indispensable role in both theory and application.However,dependent functional data are always being missing at random(MAR)during measurement or storage.So the problem for statistics modeling in MAR is significant to study.This dissertation is mainly focused on responses complete and MAR.In this paper,the kNN nonparametric regression model of functional dependent data and its asymptotic properties are studied,and the estimation results are verified by simulation and real data.The main contents are as follows:(1)Nonparametric kNN regression estimation of functional dependent samplesIn this part,we first give the kNN estimation for functional nonparametric regression models under dependent samples.The NW kernel method and kNN method of functional nonparametric regression are studied by simulation and real data of sea surface temperature,respectively.The validity of kNN method is illustrated in finite dimension.(2)Nonparametric kNN regression estimation of functional dependent samples with responses missing at random.The main work of this part is to study the kNN nonparametric regression model when the functional explanatory variables have dependent structure and responses missing at random.Firstly,the estimation of the model and the uniform convergence rate of the kNN operator are given.Then a simulation study is carried out to illustrate the effect of the nonparametric kNN method with missing data.The strict proof of the uniform convergence rate of the KNN operator is given at last.