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Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 400–413 | Cite as

A Modification of Silverman’s Method for Smoothed Functional Principal Components Analysis

  • S. Mohammad E. Hosseini-Nasab
Article

Abstract

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 Silverman’s method for SFPCA. Then we give a modification of the Silverman’s 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.

Keywords

Eigenfunction Eigenvalue Functional data analysis Smoothed functional principal component analysis Stochastic expansion 

AMS Subject Classification

62H25 62M99 60H25 

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Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesShahid Beheshti UniversityTehranIran

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