On positive association of absolute-valued and squared multivariate Gaussians beyond MTP2

Helmut Finner and Markus Roters

Journal of Multivariate Analysis, 2024, vol. 202, issue C

Abstract: We show that positively associated squared (and absolute-valued) multivariate normally distributed random vectors need not be multivariate totally positive of order 2 (MTP2) for p≥3. This result disproves Theorem 1 in Eisenbaum (2014, Ann. Probab.) and the conjecture that positive association of squared multivariate normals is equivalent to MTP2 and infinite divisibility of squared multivariate normals. Among others, we show that there exist absolute-valued multivariate normals which are conditionally increasing in sequence (CIS) (or weakly CIS (WCIS)) and hence positively associated but not MTP2. Moreover, we show that there exist absolute-valued multivariate normals which are positively associated but not CIS. As a by-product, we obtain necessary conditions for CIS and WCIS of absolute normals. We illustrate these conditions in some examples. With respect to implications and applications of our results, we show PA beyond MTP2 for some related multivariate distributions (chi-square, t, skew normal) and refer to possible conservative multiple test procedures and conservative simultaneous confidence bounds. Finally, we obtain the validity of the strong form of Gaussian product inequalities beyond MTP2.

Keywords: Gaussian correlation conjecture; Infinite divisibility; Laguerre’s rule of signs; Multiple hypothesis testing; Positive association (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X24000022
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:202:y:2024:i:c:s0047259x24000022

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2024.105295

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().