Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction

Michel Denuit and Christian Y. Robert

Journal of Multivariate Analysis, 2021, vol. 186, issue C

Abstract: In Efron (1965), Efron studied the stochastic increasingness of the vector of independent random variables entering a sum, given the value of the sum. Precisely, he proved that log-concavity for the distributions of the random variables ensures that the vector becomes larger (in the sense of the usual multivariate stochastic order) when the sum is known to increase. This result is known as Efron’s “monotonicity property”. Under the condition that the random variables entering in the sum have density functions with bounded second derivatives, we investigate whether Efron’s monotonicity property generalizes when sums involve a large number of terms to which a central-limit theorem applies.

Keywords: Central-limit theorem; Log-concavity; Stochastic dominance; Stochastic increasingness (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X21000816
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:186:y:2021:i:c:s0047259x21000816

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.2021.104803

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 ().