Estimation In Generalized Partially Functional Linear Model With Multiple Functional Covariates

With the development of technology,data in various fields such as meteorology,medicine and economy have obvious functional characteristics,so they are called functional data.Traditional statistical methods have many problems in dealing with such data,which not only cause the curse of dimensionality,but also lose the sample information.Therefore,methodologies of functional data analysis(FDA)have been proposed for such data.The basic idea of FDA is to consider the observations as a function.Now,many traditional statistical methods have been applied in the framework of FDA,and in particular,functional linear regression is a fundamental problem of interest.Generalized partially functional linear model is a generalization of functional linear regression model.The model incorporates both functional predictors and scalar covariates,so it has been received increasing attention in many fields.Many existing researches focus on the analysis of generalized partially linear model using one functional predictor only.However,with the development of technology,two or more functional covariates can be collected in various fields.Therefore,we propose a generalized partially functional linear regression model with multiple functional predictors and develop the maximum quasi-likelihood estimation method of the proposed model.We also develop the aymptotical properties of the parametric estimation and derive the rates of the convergence for the estimations of the slope fucntions.In this paper,the maximum quasi-likelihood estimations of the proposed model are obtained based on functional principal component analysis.The asymptotical properties of the estimations for parametric coefficients are established and the rates of convergence for the estimations of the slope fucntions are also developed.The performances of the proposed procedure are illustrated via simulation studies and a real data example obtained from hyoid bone movement analysis.Technical proofs of the theoretical results are given in this paper.