Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices

Genest, Christian; Ouimet, Frédéric

doi:10.1016/j.jmaa.2022.126951

Cited by 6 publications

(4 citation statements)

References 39 publications

(62 reference statements)

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“…It was reframed in the above Gaussian setting by Frenkel (2008). Readers may refer to Genest et al (2024) for a brief survey of currently known results and to Herry et al (2024) for the latest advancement.…”

Section: An Open Problemmentioning

confidence: 99%

“…One motivation for obtaining a formula for (3) is its potential utility in tackling the Wishart analogue of the Gaussian product inequality conjecture, proposed by Genest et al (2024). The conjecture is stated below for convenience.…”

Section: An Open Problemmentioning

confidence: 99%

“…Theorem 1 is stated and proved in Section 4. In Section 5, Wilks' open problem of evaluating the joint moments of disjoint principal minors of Wishart random matrices is restated and further motivated by its relationship with the Gaussian product inequality conjecture described, for example, by Genest et al (2024).…”

Section: Introductionmentioning

confidence: 99%

“…of Wishart random matrices is restated and further motivated by its relationship with the Gaussian product inequality conjecture described, for example, by Genest et al (2024).…”

mentioning

confidence: 99%

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On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices

Genest,

Ouimet,

Richards

2024

Stat

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In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little‐known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture.

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Section: An Open Problemmentioning

confidence: 99%

Section: An Open Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…of Wishart random matrices is restated and further motivated by its relationship with the Gaussian product inequality conjecture described, for example, by Genest et al (2024).…”

mentioning

confidence: 99%

See 2 more Smart Citations