A combinatorial proof of the Gaussian product inequality beyond the MTP2 case

Genest Christian () and Ouimet Frédéric ()
Additional contact information
Genest Christian: Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec), Canada H3A 0B9
Ouimet Frédéric: Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec), Canada H3A 0B9

Dependence Modeling, 2022, vol. 10, issue 1, 236-244

Abstract: A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X = ( X 1 , … , X d ) {\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a linear combination, with coefficients of identical sign, of the components of a standard Gaussian random vector. This condition on X {\boldsymbol{X}} is shown to be strictly weaker than the assumption that the density of the random vector ( ∣ X 1 ∣ , … , ∣ X d ∣ ) \left(| {X}_{1}| ,\ldots ,| {X}_{d}| ) is multivariate totally positive of order 2, abbreviated MTP 2 {\text{MTP}}_{2} , for which the GPI is already known to hold. Under this condition, the paper highlights a new link between the GPI and the monotonicity of a certain ratio of gamma functions.

Keywords: complete monotonicity; gamma function; Gaussian product inequality; Gaussian random vector; moment inequality; multinomial; multivariate normal; polygamma function (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/demo-2022-0116 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:10:y:2022:i:1:p:236-244:n:10

DOI: 10.1515/demo-2022-0116

Access Statistics for this article

Dependence Modeling is currently edited by Giovanni Puccetti

More articles in Dependence Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().