×

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.

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