Statistics Papers

Document Type

Journal Article

Date of this Version

2008

Publication Source

Electronic Journal of Statistics

Volume

2

Start Page

678

Last Page

695

DOI

10.1214/08-EJS218

Abstract

Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we propose an alternative approach to FPCA using penalized rank one approximation to the data matrix. Our contributions are four-fold: (1) by considering invariance under scale transformation of the measurements, the new formulation sheds light on how regularization should be performed for FPCA and suggests an efficient power algorithm for computation; (2) it naturally incorporates spline smoothing of discretized functional data; (3) the connection with smoothing splines also facilitates construction of cross-validation or generalized cross-validation criteria for smoothing parameter selection that allows efficient computation; (4) different smoothing parameters are permitted for different FPCs. The methodology is illustrated with a real data example and a simulation.

Keywords

functional data analysis, penalization, regularization, singular value decomposition

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Date Posted: 27 November 2017

This document has been peer reviewed.