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

Abstract

This note reports partial results related to the Gaussian product inequality (GPI) conjecture for the joint distribution of traces of Wishart matrices. In particular, several GPI-related results from Wei (2014) and Liu et al. (2015) are extended in two ways: by replacing the power functions with more general classes of functions, and by replacing the usual Gaussian and multivariate gamma distributional assumptions by the more general trace-Wishart distribution assumption. These findings suggest that a Kronecker product form of the GPI holds for diagonal blocks of any Wishart distribution.

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References in corpus (2)

• Squared chaotic random variables: new moment inequalities with applications
• A combinatorial proof of the Gaussian product inequality beyond the MTP${}_2$ case

Cited by in corpus (2)

• A short proof of the strong three dimensional Gaussian product inequality
• On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices