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October 1996 Cone order association and stochastic cone ordering with applications to order-restricted testing
Arthur Cohen, H. B. Sackrowitz
Ann. Statist. 24(5): 2036-2048 (October 1996). DOI: 10.1214/aos/1069362308

Abstract

Cohen, Sackrowitz and Samuel-Cahn introduced the notion of cone order association and established a necessary and sufficient condition for a normal random vector to be cone order associated (COA). In this paper we provide the following: (1) a necessary and sufficient condition for a multinomial distribution to be COA when the cone is a pairwise contrast cone; (2) a relationship between COA and regular association; (3) a notion of stochastic cone ordering (SCO) of random vectors along with two preservation theorems indicating monotonicity properties of expectations as functions of parameters; and (4) applications to unbiasedness of tests and monotonicity of power functions of tests in cone order-restricted hypothesis-testing problems. In particular, the matrix order alternative hypothesis-testing problem is treated when the underlying distributions are independent Poisson or the joint distribution is multinomial.

Citation

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Arthur Cohen. H. B. Sackrowitz. "Cone order association and stochastic cone ordering with applications to order-restricted testing." Ann. Statist. 24 (5) 2036 - 2048, October 1996. https://doi.org/10.1214/aos/1069362308

Information

Published: October 1996
First available in Project Euclid: 20 November 2003

zbMATH: 0898.62073
MathSciNet: MR1421159
Digital Object Identifier: 10.1214/aos/1069362308

Subjects:
Primary: 62H99
Secondary: 62F03

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 5 • October 1996
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