School Seminars and Colloquia

Some Properties of Principal Components Analysis for Functional Data

Joint Applied Statistics / Complex Systems Seminar

by Mohammad Hosseini-Nasab

Institution: Australian National University
Date: Thu 1st December 2005
Time: 2:15 PM
Location: Theatre 2, Old Geology Building, University of Melbourne

Abstract: Functional data analysis is intrinsically infinite-dimensional; functional principal component analysis, or PCA, reduces dimension to a finite level, and points to the most significant components of the
data. However, while this technique is often discussed, its properties are not as well understood as they might be. In this talk, it is shown how the properties of functional PCA can be elucidated through stochastic expansions and related results. The approach quantifies the errors that arise
through statistical approximation, in successive terms of orders $n^{-1/2}, n^{-1}, n^{-3/2}$,..., where $n$ denotes sample size. The expansions show how spacings among eigenvalues impact on statistical performance. The results can be used to explore properties of existing methods, and also to suggest new techniques. In particular, we suggest bootstrap methods for constructing simultaneous confidence regions for an infinite number of eigenvalues, and also for individual eigenvalues and eigenvectors.

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