Functional Regression Estimation with Application to Sparsely Observed Data

• Activity Number: 153 - Recent Developments in Functional Data Analysis and Empirical Likelihood Methods in Biostatistics
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Ao Yuan* and Hongbin Fang and Ming T Tan
• Companies: Georgetown University and Georgetown University and Georgetown University
• Keywords: Functional data ; hypothesis testing ; regression function ; reproducing kernel Hilbert space

Abstract

Consider the regression model in which the response, covariates and the regression coefficients are all functions of time. This is more general than most existing functional regression models, in which either the response or the coefficient(s) are independent of time. We propose and study such functional regression problem using method of reproducing kernel Hilbert space. The estimation of the regression functions are constructed using penalized least squares estimate, basic asymptotic properties of the estimator are investigated, and hypothesis testing of regression coefficients are considered. Simulation studies are conducted to evaluate the performance of the proposed method, compared it with the kernel smoothing and spline methods, and shows advantage of the proposed method. The method is then used to analyses a real functional data for illustration.