Generalizations of Efron’s theorem

Yannis Oudghiri

Statistics & Probability Letters, 2021, vol. 177, issue C

Abstract: In this article, we prove two new versions of a theorem proven by Efron in Efron (1965). Efron’s theorem says that if a function ϕ:R2→R is non-decreasing in each argument then we have that the function s↦E[ϕ(X,Y)|X+Y=s] is non-decreasing. We name restricted Efron’s theorem a version of Efron’s theorem where ϕ:R→R only depends on one variable. PFn is the class of functions such as ∀a1≤⋯≤an,b1≤⋯≤bn,det(f(ai−bj))1≤i,j≤n≥0. The first version generalizes the restricted Efron’s theorem for random variables in the PFn class. The second one considers the non-restricted Efron’s theorem with a stronger monotonicity assumption. In the last part, we give a more general result of the second generalization of Efron’s theorem.

Keywords: Log-concavity; Efron’s theorem; Andreev’s formula (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221001206
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:177:y:2021:i:c:s0167715221001206

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.2021.109158

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 ().