A modification of silvermans method for smoothed functional principal components analysis

Statistical procedures for analyzing data that are in the form of curves and of infinite dimension are provided by functional data analysis. Functional principal component analysis is widely used in the study of functional data, since it allows finite-dimensional analysis of a problem that is intrinsically infinite dimensional. In this article, when considering smoothed functional principal component analysis (SFPCA), we first briefly review Silvermans method for SFPCA. Then we give a modification of the Silvermans method for SFPCA and investigate the performance of the modification through stochastic expansions. The modification is based on considering another parameter with the smoothing parameter proposed by Silverman (1996). We study the consistency under suitable conditions theoretically and show that adding the new parameter partly improves the performance of the eigenfunctions estimators toward having smaller error. We also show this improvement through a simulation study, numerically. Copyright © Grace Scientific Publishing, LLC.