For normal models we consider the problem of testing a null hypothesis against an order-restricted alternative. The alternative always consists of a cone minus the null space. We offer sufficient conditions for a class of tests to be complete and for unbiasedness of tests. Both sets of sufficient conditions are expressed in terms of the notion of cone order monotonicity. A method of constructing tests that are unbiased and in the complete class is given. The method yields new tests of value to many problems. Detailed applications and a simulation study are offered for testing homogeneity of means against the simple order alternative and for testing homogeneity against the matrix order alternative.
Publié le : 1995-12-14
Classification:
Bayes-type tests,
complete class,
cone order monotonicity,
cone ordering,
convexity,
dual cone,
likelihood ratio test,
matrix order alternative,
unbiased tests
@article{1193758709,
author = {Cohen, Arthur and Sackrowitz, Harold B. and Samuel-Cahn, Ester},
title = {Constructing tests for normal order-restricted inference},
journal = {Bernoulli},
volume = {1},
number = {3},
year = {1995},
pages = { 321-333},
language = {en},
url = {http://dml.mathdoc.fr/item/1193758709}
}
Cohen, Arthur; Sackrowitz, Harold B.; Samuel-Cahn, Ester. Constructing tests for normal order-restricted inference. Bernoulli, Tome 1 (1995) no. 3, pp. 321-333. http://gdmltest.u-ga.fr/item/1193758709/