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Novel whitening approaches in functional settings

Marc Vidal (UGent) and Ana M. Aguilera
(2023) STAT. 12(1).
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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.
Keywords
functional data, RKHS, correlation operator, cross-covariance operator, functional independent component analysis, Mahalanobis distance, sphering, whitening operator

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Citation

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MLA
Vidal, Marc, and Ana M. Aguilera. “Novel Whitening Approaches in Functional Settings.” STAT, vol. 12, no. 1, 2023, doi:10.1002/sta4.516.
APA
Vidal, M., & Aguilera, A. M. (2023). Novel whitening approaches in functional settings. STAT, 12(1). https://doi.org/10.1002/sta4.516
Chicago author-date
Vidal, Marc, and Ana M. Aguilera. 2023. “Novel Whitening Approaches in Functional Settings.” STAT 12 (1). https://doi.org/10.1002/sta4.516.
Chicago author-date (all authors)
Vidal, Marc, and Ana M. Aguilera. 2023. “Novel Whitening Approaches in Functional Settings.” STAT 12 (1). doi:10.1002/sta4.516.
Vancouver
1.
Vidal M, Aguilera AM. Novel whitening approaches in functional settings. STAT. 2023;12(1).
IEEE
[1]
M. Vidal and A. M. Aguilera, “Novel whitening approaches in functional settings,” STAT, vol. 12, no. 1, 2023.
@article{8770510,
  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.}},
  articleno    = {{e516}},
  author       = {{Vidal, Marc and Aguilera, Ana M.}},
  issn         = {{2049-1573}},
  journal      = {{STAT}},
  keywords     = {{functional data,RKHS,correlation operator,cross-covariance operator,functional independent component analysis,Mahalanobis distance,sphering,whitening operator}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{10}},
  title        = {{Novel whitening approaches in functional settings}},
  url          = {{http://doi.org/10.1002/sta4.516}},
  volume       = {{12}},
  year         = {{2023}},
}
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