Directional tests for one-sided alternatives in multivariate models

Arthur Cohen, Harold B. Sackrowitz

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Consider one-sided testing problems for a multivariate exponential family model. Through conditioning or other considerations, the problem oftentimes reduces to testing a null hypothesis that the natural parameter is a zero vector against the alternative that the natural parameter lies in a closed convex cone ℓ. The problems include testing homogeneity of parameters, testing independence in contingency tables, testing stochastic ordering of distributions and many others. A test methodology is developed that directionalizes the usual test procedures such as likelihood ratio, chi square, Fisher, and so on. The methodology can be applied to families of tests where the family is indexed by a size parameter so as to enable nonrandomized testing by p-values. For discrete models, a refined family of tests provides a refined grid for better testing by p-values. The tests have essential monotonicity properties that are required for admissibility and for desirable power properties. Two examples are given.

Original languageEnglish (US)
Pages (from-to)2321-2338
Number of pages18
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 1998

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Contingency tables
  • Fisher's test
  • Independence
  • Likelihood ratio order
  • Multivariate exponential family
  • Order restricted inference
  • Peeling
  • Stochastic order
  • Wilcoxon-Mann-Whitney test


Dive into the research topics of 'Directional tests for one-sided alternatives in multivariate models'. Together they form a unique fingerprint.

Cite this