Spline Estimation of Functional Principal Components via Manifold Conjugate Gradient Algorithm

• Activity Number: 521 - Statistical Methods for Functional Data
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hanxuan Ye* and Shiyuan He and Kejun He
• Companies: Texas A&M University and Renmin University of China and Renmin University of China
• Keywords: Functional data analysis; Product manifold ; Stiefel manifold ; Conjugate gradient algorithm

Abstract

Functional principal component analysis has become the most important dimension reduction technique in functional data analysis. Based on B-spline approximation, functional principal components (FPCs) can be efficiently estimated by the expectation-maximization (EM) and the geometric restricted maximum likelihood (REML) algorithms under the strong assumption of Gaussianity on the principal component scores and observational errors. The EM algorithm does not exploit the underlying geometric manifold structure, while the performance of REML is known of being unstable. In this article, We propose a conjugate gradient algorithm over the product manifold to estimate FPCs. This algorithm exploits the manifold geometry structure of the overall parameter space, thus improving its search efficiency and estimation accuracy. We also show that a roughness penalization can be easily incorporated into our algorithm with a potentially better fit. The appealing numerical performance of the proposed method is demonstrated by simulation studies and the analysis of the real data.