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December, 1992 Invariant Directional Orderings
E. L. Lehmann, J. Rojo
Ann. Statist. 20(4): 2100-2110 (December, 1992). DOI: 10.1214/aos/1176348905


Statistical concepts of order permeate the theory and practice of statistics. The present paper is concerned with a large class of directional orderings of univariate distributions. (What do we mean by saying that a random variable $Y$ is larger than another random variable $X$?) Attention is restricted to preorders that are invariant under monotone transformations; this includes orderings such as monotone likelihood ratio, hazard ordering, and stochastic ordering. Simple characterizations of these orderings are obtained in terms of a maximal invariant. It is shown how such invariant preorderings can be used to generate concepts of $Y_2$ being further to the right of $X_2$ than $Y_1$ is of $X_1$.


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E. L. Lehmann. J. Rojo. "Invariant Directional Orderings." Ann. Statist. 20 (4) 2100 - 2110, December, 1992.


Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0776.62011
MathSciNet: MR1193328
Digital Object Identifier: 10.1214/aos/1176348905

Primary: 62A05
Secondary: 60E05, 62B15, 62E10

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 4 • December, 1992
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