Statistical Inference Of Partial Functional Models

In the era of big data,with the development of technology for collecting and storing data,the data obtained is becoming more and more complex.Functional data is one of the complex data with functional characteristics.In the modeling and analysis of functional data,we will encounter such a situation,some covariates are functional data,and some covariates are real-valued.Based on such mixed data,this paper studies the parameter estimation problem of the single-index partial functional model.First,using K-L(Karhunan-Loève)expansion to expand the functional covariate representation,obtaining the eigenvalue and eigenfunction of the covariance function,and combining the functional principal component analysis method to estimate the function part of the model and the unknown slope function;second,using cubic B-sample to estimate the connection function of the single index part;the index parameters are handled by the ”remove one component” method,and then it is estimated by the LevenbergMarquardt iterative optimization method;finally,it is combined with the least squares estimation method.The loss function gives an estimate of the model.Under certain assumptions,the convergence rate of the estimated parameter of the model is given.At the same time,the asymptotic normality and consistency of the obtained estimates are proved.