Partial Functional Linear Regression Model And Estimation

Functional data is the data that in the form of function.The biggestcharacteristic of functional data is that the data is function.The startingpoint of functional data is considering the data as a separate item,notas a series of points at diferent time.Because of the particularity of thefunctional data,it won’t get a good result when we apply the classical mul-tiple regression method into functional data.So there are many solutionsdeveloping to the problem.Considering the data observed as an element of an infinite dimension-al functional space is the basic idea of functional data analysis(FDA).Withthe rapid development of science and technology in the recent20years,functional data analysis has been playing a more and more important rolein modern scientific research.Many research area encounter the statisticalproblems about functional data analysis,such as Psychology,Economics,Weather forecast,Medical diagnosis,Life science and Children growth anal-ysis,and so on.Compared to classical multivariate statistical methods andtools, functional data analysis is still in the initial development period,and the application prospect is very broad.The paper mainly discuss the methods to estimate the functional pa-rameters of the partial functional linear regression model. We introducethe concept step by step for the purpose of helping the readers under-stand functional data better,and thus understand the main idea of thispaper.So we do a lot of work in preview,especially in the section of linearmodel.We sum up the predecessors’ estimating method.The main content of this article,presmoothing estimation method,is proposed on the basis ofpredecessors’ research results too.Most of the paper is the research resultsduring my Master’s study.Presmoothing estimation,comes from the idea of paper one. We s-tudy the partial functional linear model by using pre-smoothing tech-nique.In the model,the response is scalar and explanatory variables con-sist of finite dimensional vector and functional variables value in func-tional space. We not only access the estimators,but also discuss theirconsistency.At the end of the paper,we show the efect of the estimatorsby numerical simulation,compared with the other estimator.As we can seefrom the results,the presmoothing estimator has a strong robustness.Thatis the meaning of this paper.