# Some Properties of Principal Components Analysis for Functional Data

Joint Applied Statistics / Complex Systems Seminar

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.