Study On Problems Of Functional Linear Regression Models

Based on statistical analysis of functional data regression model is one of hotresearch fields on mathematical statistics. This paper studies the estimate problemof a special functional partial linear regression model and construct the estimator ofthe parameters.We obtained the asymptotic properties of the estimator based oncorrelated error.Then the estimator of linear operator about functional regressionmodel is investigated under fixed design while the explanatory variables andresponse variables are functional.We established the complete convergence rate ofthe estimator.Our results generalize the existing results in the literature.This paper is divided into five chapters:In the first and second chapters:Mainly discussed the research background andstatus of development on functional regression model,some preliminaries anddifferent functional models is given.In the third chapter:The estimation of the parameter under correlated error isgiven in functional partial linear model,use K-L representation to deal with thefunctional variables,then the estimator and asymptotic properties are given by usingfunctional principal components analysis,our results extend and improve someknown ones.In the fourth chapter:The functional regression model is investigated while theexplanatory variables and response variables are functional.EstimatorT nof thelinear operator T is given under fixed design,the convergence rate of the estimatoris given under completely convergence. The work of this part is complementary ofthe existing references and results.In the fifth chapter:We give the whole analysis and summarize of the paper.