The Estimation Of Nonparametric Functional Kernel Regression On Several Issues Is Studied

Functional regression model is the most important statistics models in FDA,when we explore the relationship between a functional explanatory variable and a scalar response variable.And functional nonparametric regression is the one of the commonly model used in the functional regression model.In real life,the most common occurrence is time series data,which is not independent.We call it dependent sample data.Because of various factors,response variables are often missing at random(MAR)in practical work such as sampling survey,pharmaceutical tracing test,reliability test and so on,therefore the problem for statistics models in MAR is significant to study.So,this paper is mainly based on nonparametric regression model,for dependent samples,we use the method of kernel structure estimators,and study asymptotic properties of estimators when responses missing at random(MAR)or responses are functional,respectively.Finally,the results are verified by a simulation experiment.The main contents are given as follow:(1)This section is mainly based on nonparametric regression model,where the explanatory variable is defined in a semi-metric space and the response variable is evaluated in Hilbert space.The main work of this part is to take the functional response into consideration,constructing kernel estimator,and we obtain the pointwise almost complete convergence and the rates of uniform almost complete convergence of the estimator.Finally,a simulation study is carried out to illustrate the finite sample performance of the estimator is very good.(2)This section also focuses on the nonparametric regression model,where the response variable Y is scalar with missing at random(MAR)and the explanatory variable X taking values in a semi-metric abstract space F.The main aim of this work is to estimate regression operator by nonparametric kernel method and prove the uniform almost complete convergence of estimator under dependent data.These research are(or will be)key tools for many cases of missing data in functional data analysis.