Novel whitening approaches in functional settings
Metadata
Show full item recordEditorial
Wiley
Materia
Correlation operator Cross-covariance operator Functional independent component analysis Mahalanobis distance Sphering Whitening operator
Date
2022-10-19Referencia bibliográfica
Vidal, M., & Aguilera, A. M. (2023). Novel whitening approaches in functional settings. Stat, 12( 1), e516. [https://doi.org/10.1002/sta4.516]
Sponsorship
Ministry of Science and Innovation, Spain (MICINN) Instituto de Salud Carlos III Spanish Government PID2020-113961GB-I00; Methusalem, Vlaamse regeringAbstract
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.