The linear stochastic order and directed inference for multivariate ordered distributions

Ori Davidov, Shyamal Peddada

Research output: Contribution to journalArticlepeer-review


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 prechronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP).

Original languageEnglish
Pages (from-to)1-40
Number of pages40
JournalAnnals of Statistics
Issue number1
StatePublished - Feb 2013


  • Nonparametric tests
  • Order-restricted statistical inference
  • Stochastic order relations

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'The linear stochastic order and directed inference for multivariate ordered distributions'. Together they form a unique fingerprint.

Cite this