Estimation For Partial Functional Linear Model Under Sparse Design

Functional data analysis(FDA)has received more and more attention over the past few decades,where each individual or unit of these data can be approximated as a curve.Functional data can be divided into dense and sparse functional data,in which sparse functional data refers to the sparse and irregular data with measurement error.Func-tional regression is an important research topic in FDA.However,most of the current researches on functional regression models are confined to completely or densely observed functional data.The researches of functional regression for sparse design are very few.In this paper,we focus on the estimation of the partial functional linear model for sparse design.The functional principal component analysis(FPCA)and local linear method in nonparametric statistics will be used to obtain the estimation of the parameters and the slope function in the model.Also,we extend the definition of coefficients of determination in linear regression to partial functional linear model and give the estimation method.Fi-nally,the numerical simulation will be used to show that the proposed method has a very good finite sample property.