zbMATH — the first resource for mathematics

Cone order association and stochastic cone ordering with applications to order-restricted testing. (English) Zbl 0898.62073
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.

62H20 Measures of association (correlation, canonical correlation, etc.)
62H99 Multivariate analysis
62F03 Parametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
Full Text: DOI