The Gaussian product inequality conjecture for multinomial covariances
Probability
2023-08-24 v4 Statistics Theory
Statistics Theory
Abstract
In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These covariance matrices are relevant since their off-diagonal elements are negative, which is the hardest case to cover for the GPI conjecture, as mentioned by [Russell, O., \& Sun, W. 2022. Some new {G}aussian product inequalities. {\em J. Math. Anal. Appl.}, {\bf 515}(2), Paper No. 126439, 21 pp.].
Keywords
Cite
@article{arxiv.2209.01505,
title = {The Gaussian product inequality conjecture for multinomial covariances},
author = {Frédéric Ouimet},
journal= {arXiv preprint arXiv:2209.01505},
year = {2023}
}
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