The Annals of Statistics

The linear stochastic order and directed inference for multivariate ordered distributions

Ori Davidov and Shyamal Peddada

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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).

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Ann. Statist., Volume 41, Number 1 (2013), 1-40.

First available in Project Euclid: 5 March 2013

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 62E20: Asymptotic distribution theory 62G10: Hypothesis testing 62G20: Asymptotic properties 62H99: None of the above, but in this section 62P15: Applications to psychology

Nonparametric tests order-restricted statistical inference stochastic order relations


Davidov, Ori; Peddada, Shyamal. The linear stochastic order and directed inference for multivariate ordered distributions. Ann. Statist. 41 (2013), no. 1, 1--40. doi:10.1214/12-AOS1062.

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