Open Access
February 2013 The linear stochastic order and directed inference for multivariate ordered distributions
Ori Davidov, Shyamal Peddada
Ann. Statist. 41(1): 1-40 (February 2013). DOI: 10.1214/12-AOS1062


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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Ori Davidov. Shyamal Peddada. "The linear stochastic order and directed inference for multivariate ordered distributions." Ann. Statist. 41 (1) 1 - 40, February 2013.


Published: February 2013
First available in Project Euclid: 5 March 2013

zbMATH: 1266.60029
MathSciNet: MR3059408
Digital Object Identifier: 10.1214/12-AOS1062

Primary: 60E15 , 62E20 , 62G10 , 62G20 , 62H99 , 62P15

Keywords: nonparametric tests , order-restricted statistical inference , stochastic order relations

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • February 2013
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