Constructing tests for normal order-restricted inference

Arthur Cohen, Harold Sackrowitz, Ester Samuel-Cahn

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

For normal models we consider the problem of testing a null hypothesis against an order-restricted alternative. The alternative always consists of a cone minus the null space. We offer sufficient conditions for a class of tests to be complete and for unbiasedness of tests. Both sets of sufficient conditions are expressed in terms of the notion of cone order monotonicity. A method of constructing tests that are unbiased and in the complete class is given. The method yields new tests of value to many problems. Detailed applications and a simulation study are offered for testing homogeneity of means against the simple order alternative and for testing homogeneity against the matrix order alternative.

Original languageEnglish (US)
Pages (from-to)321-333
Number of pages13
JournalBernoulli
Volume1
Issue number4
DOIs
StatePublished - Jan 1 1995

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Bayes-type tests
  • Complete class
  • Cone order monotonicity
  • Cone ordering
  • Convexity
  • Dual cone
  • Likelihood ratio test
  • Matrix order alternative
  • Unbiased tests

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