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.
Publié le : 1996-10-14
Classification:
Cone order monotonicity,
dual cone,
multinomial distribution,
pairwise contrast cone,
matrix order alternative,
preservation theorem,
62H99,
62F03
@article{1069362308,
author = {Cohen, Arthur and Sackrowitz, H. B.},
title = {Cone order association and stochastic cone ordering with applications to order-restricted testing},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 2036-2048},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362308}
}
Cohen, Arthur; Sackrowitz, H. B. Cone order association and stochastic cone ordering with applications to order-restricted testing. Ann. Statist., Tome 24 (1996) no. 6, pp. 2036-2048. http://gdmltest.u-ga.fr/item/1069362308/