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On conditional stochastic ordering of distributions

Published online by Cambridge University Press:  01 July 2016

Ludger Rüschendorf
Ludger Rüschendorf*
Affiliation:
University of Münster
*
∗Postal address: Institut für Mathematische Statistik, Westfalische Wilhelms-Universität, Einsteinstrasse 62, W-4400 Münster, Germany.
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Abstract

Conditional stochastic ordering is concerned with the stochastic ordering of a pair of probability measures conditional on certain subsets or sub-σ -algebras. Some basic results of conditional stochastic ordering were proved by Whitt. We extend some of Whitt's results and prove a basic relation between stochastic ordering conditional on subsets and stochastic ordering conditional on σ -algebras. In the second part of the paper we consider the ordering of conditional expectations. There are several different formulations of this problem motivated by different types of applications.

Keywords

MONOTONE LIKELIHOOD RATIOMAXIMAL INEQUALITIESASSOCIATION
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 1 , March 1991 , pp. 46 - 63
Copyright
Copyright © Applied Probability Trust 1991 

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