title: The linear stochastic order and directed inference for multivariate ordered distributions.
abstract: 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).
authors.affiliation: Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905 Israel.
authors.forename: Ori
authors.initials: O
authors.lastname: Davidov
authors.forename: Shyamal
authors.initials: S
authors.lastname: Peddada
keywords: nonparametric tests; order restricted statistical inference; stochastic order relations
references.citation: Natl Toxicol Program Tech Rep Ser. 2003 Jan;(505):1-268
references.pmid: 12637974
references.citation: J Biopharm Stat. 2009;19(2):247-55
references.pmid: 19212877
references.citation: J Am Stat Assoc. 2011;106(496):1394-1404
references.pmid: 22973069