Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods

• 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): Hongbin Fang* and Ming Xiong and Ao Yuan and Ming T Tan and Colin O. Wu
• Companies: Georgetown University and Central China Normal University and Georgetown University and Georgetown University and Office of Biostatistics Research, National Heart, Lung and Blood Institute, NIH
• Keywords: Mean curve estimation ; Hypothesis testing ; Functional data ; Reproducing kernel Hilbert space ; Kernel function ; Asymptotic property

Abstract

Functional data analysis has important applications in biomedical, and genetic studies and other areas. Existing statistical methods of functional data analysis have mostly focused on the estimation and hypothesis testing of functional curves using local smoothing estimators or some known basis approximations. However, those methods may result in a biased estimation or relative large variance of the estimator when the observation time points are unbalanced. In this paper, we propose reproducing kernel Hilbert space (RKHS) approaches to estimate mean curves of functional data. Although the methods of RKHS have been employed in regression analysis for functional data, this paper provides a general theoretical approach of mean estimation with functional data using RKHS. The simulation studies show that the RKHS approach has a better performance than the conventional methods, such as local weighted polynomial regression and splines, when the observation time points are unbalanced. Furhtermore, based on the RKHS approach, we propose two statistics for testing equality of mean curves from two populations and a mean curve belonging to some subspace, respectively.