Functional Principal Component Analysis with Long-Range Dependent Errors

• Activity Number: 355
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jan Beran and Haiyan Liu* and Klaus Telkmann
• Companies: University of Konstanz and Universitaet Konstanz and Universitaet Konstanz
• Keywords: functional principal component analysis ; two sample inference ; long range dependence

Abstract

We consider estimation of eigenvalues, eigenfunctions and scores in functional data analysis (FDA), with the modification that the random curves are perturbed by error processes that exhibit short- or long-range dependence. As it turns out, the asymptotic distribution of estimated eigenvalues and estimated eigenfunctions does not depend on the dependence structure of the error process. However, the rate of convergence and the asymptotic distribution of estimated scores differ distinctly between the cases of short and long memory. Two sample inference in FDA is also discussed. A test statistic for testing the equality of eigenspaces is constructed and asymptotic properties are derived. Numerical examples illustrate the results.