A Gaussian expectation product inequality

Zhenxia Liu, Zhi Wang and Xiangfeng Yang

Statistics & Probability Letters, 2017, vol. 124, issue C, 1-4

Abstract: Let (X1,…,Xn) be any n-dimensional centered Gaussian random vector, in this note the following expectation product inequality is proved: E∏j=1nfj(Xj)≥∏j=1nEfj(Xj) for functions fj,1≤j≤n, taking the forms fj(x)=∫0∞cos(xu)μj(du), where μj,1≤j≤n, are finite positive measures. The motivation of studying such an inequality comes from the Gaussian correlation conjecture (which was recently proved) and the Gaussian moment product conjecture (which is still unsolved). Several explicit examples of such functions fj are given. The proof is built on characteristic functions of Gaussian random variables.

Keywords: Gaussian random vector; Bochner’s theorem; Gaussian expectation product inequality (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715217300044
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:stapro:v:124:y:2017:i:c:p:1-4

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.spl.2016.12.018

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().