A phase transition for the probability of being a maximum among random vectors with general iid coordinates

Royi Jacobovic and Or Zuk

Statistics & Probability Letters, 2023, vol. 199, issue C

Abstract: Consider n iid real-valued random vectors of size k having iid coordinates with a general distribution function F. A vector is a maximum if and only if there is no other vector in the sample that weakly dominates it in all coordinates. Let pk,n be the probability that the first vector is a maximum. The main result of the present paper is that if k≡kn grows at a slower (faster) rate than a certain factor of log(n), then pk,n→0 (resp. pk,n→1) as n→∞. Furthermore, the factor is fully characterized as a functional of F. We also study the effect of F on pk,n, showing that while pk,n may be highly affected by the choice of F, the phase transition is the same for all distribution functions up to a constant factor.

Keywords: Phase transition; Multivariate maximum; Pareto; Extreme values (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715223000718
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:199:y:2023:i:c:s0167715223000718

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.2023.109847

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 ().