The linear stochastic order and directed inference for multivariate ordered distributions. (English) Zbl 1266.60029

Davidov, Ori; Peddada, Shyamal

Ann. Stat. 41, No. 1, 1-40 (2013).

Summary: Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy’s classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a 90-day pre-chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP).

MSC:

60E15	Inequalities; stochastic orderings
62E20	Asymptotic distribution theory in statistics
62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference
62H99	Multivariate analysis
62P15	Applications of statistics to psychology

Keywords:

nonparametric tests; order-restricted statistical inference; stochastic order relations

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