The Annals of Statistics

Cone order association and stochastic cone ordering with applications to order-restricted testing

Arthur Cohen and H. B. Sackrowitz

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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.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2036-2048.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362308

Digital Object Identifier
doi:10.1214/aos/1069362308

Mathematical Reviews number (MathSciNet)
MR1421159

Zentralblatt MATH identifier
0898.62073

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62F03: Hypothesis testing

Keywords
Cone order monotonicity dual cone multinomial distribution pairwise contrast cone matrix order alternative preservation theorem

Citation

Cohen, Arthur; Sackrowitz, H. B. Cone order association and stochastic cone ordering with applications to order-restricted testing. Ann. Statist. 24 (1996), no. 5, 2036--2048. doi:10.1214/aos/1069362308. https://projecteuclid.org/euclid.aos/1069362308


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