Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE ( © Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy and Legal Notice).

date: 04 April 2020

Abstract and Keywords

This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.

Keywords: principal component analysis, functional data, finite-dimensional data, infinite-dimensional data, functional linear regression, functional data analysis, dimension reduction, weighted least squares, density surrogate, log-density

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.