An Extension of a Convolution Inequality forG-Monotone Functions and an Approach to Bartholomew's Conjectures

Manabu Iwasa

Journal of Multivariate Analysis, 1996, vol. 59, issue 2, 249-271

Abstract: A variety of convolution inequalities have been obtained since Anderson's theorem. ?In this paper, we extend a convolution theorem forG-monotone functions by weakening the symmetry condition ofG-monotone functions. Our inequalities are described in terms of several orderings obtained from a cone. It is noteworthy that the orderings detect differences in directions. A special case of the orderings induces a majorization-like relation on spheres. Applying our inequality, Bartholomew's conjectures, which concern directions yielding the maximum power and the minimum power of likelihood ratio tests for order-restricted alternatives, are partly settled.

Keywords: Bartholomew's; conjecture; -test; cone; ordering; convolution; inequality; G; -monotone; function; K-decreasing; function; majorization; order; restricted; alternatives; reflection (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(96)90064-0
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:59:y:1996:i:2:p:249-271

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

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 ().