Novel whitening approaches in functional settings

Abstract

Whitening is a critical normalization method to enhance statistical reduction via reparametrization to unit covariance. This article introduces the notion of whitening for random functions assumed to reside in a real separable Hilbert space. We compare the properties of different whitening transformations stemming from the factorization of a bounded precision operator under a particular geometrical structure. The practical performance of the estimators is shown in a simulation study, providing helpful insights into their optimization. Computational algorithms for the estimation of the proposed whitening transformations in terms of basis expansions of a functional data set are also provided.