A Wavelet Approach to Functional Principal Component Analysis
F. Ocaña, Olga Valenzuela, Ana Maria Aguilera · COMPSTAT · 1998
The aim of this paper is to approximate the estimates in the principal component analysis of a continuous time stochastic process (functional PCA) by using wavelet methods. A short review of estimating in the functional PCA leads to the problem of solving the integral equation with the covariance function as kernel. An estimating procedure based on wavelet methods is then provided to obtain approximate estimates. Wavelet methods and multiresolution analysis (MRA) are jointly considered. Furthermore, MRA provides an approximating framework to estimate functional PCA when data are observed at discrete knots on a real interval. This wavelet approach is tested by simulating at discrete knots sample functions of Brownian motion. The PCA of this process is compared with those estimated by means of the wavelet approach.