Cohen, Arthur; Sackrowitz, H. B. Cone order association and stochastic cone ordering with applications to order-restricted testing. (English) Zbl 0898.62073 Ann. Stat. 24, No. 5, 2036-2048 (1996). Summary: The authors and E. Samuel-Cahn [J. Multivariate Anal. 55, No. 2, 320-330 (1995; see the preceding entry, Zbl 0898.62072)] 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). 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. Cited in 1 ReviewCited in 8 Documents MSC: 62H20 Measures of association (correlation, canonical correlation, etc.) 62H99 Multivariate analysis 62F03 Parametric hypothesis testing 62H15 Hypothesis testing in multivariate analysis Keywords:cone order monotonicity; dual cone; cone order association; multinomial distribution; pairwise contrast cone; preservation theorems; unbiasedness of tests; monotonicity of power functions; matrix order alternative Citations:Zbl 0898.62072 × Cite Format Result Cite Review PDF Full Text: DOI