2023
DOI: 10.1002/sta4.516
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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… Show more

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Cited by 3 publications
(1 citation statement)
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“…To this end, we further propose a form of deconvolution by narrowbanding the signal into two additional subbands, from 0.2 to 1 Hz ( θ2) and from 0.4 to 1 Hz ( θ3). This technique is used as an alternative to taking first differences, which although it has previously allowed to establish a number of correlations with NE axonal activity (Joshi et al, 2016; Reimer et al, 2016), after a first normalisation of the pupil data, statistical effects are more unlikely to survive when differentiating (which is also a kind of normalisation); see Discussion in Vidal and Aguilera (2023).…”
Section: Methodsmentioning
confidence: 99%
“…To this end, we further propose a form of deconvolution by narrowbanding the signal into two additional subbands, from 0.2 to 1 Hz ( θ2) and from 0.4 to 1 Hz ( θ3). This technique is used as an alternative to taking first differences, which although it has previously allowed to establish a number of correlations with NE axonal activity (Joshi et al, 2016; Reimer et al, 2016), after a first normalisation of the pupil data, statistical effects are more unlikely to survive when differentiating (which is also a kind of normalisation); see Discussion in Vidal and Aguilera (2023).…”
Section: Methodsmentioning
confidence: 99%