Directed likelihood ratio tests for ordered alternatives and inference results for the star-shaped restriction

Arthur Cohen, Harold Sackrowitz

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

To test a null hypothesis of homogeneity of parameters versus an order restricted alternative a popular method is to use a restricted likelihood ratio test. An alternative approach which oftentimes has desirable properties is a directed likelihood ratio test. In this paper, we give sufficient conditions under which these approaches coincide. We indicate cases where they do not coincide. One such case is where the parameters satisfy the lower star-shaped restriction and the underlying random variables are independent with Poisson distributions. For this model, we study and prefer the directed likelihood ratio test. We also propose estimators of the parameters which we feel are more desirable than the maximum likelihood estimators.

Original languageEnglish (US)
Pages (from-to)181-189
Number of pages9
JournalJournal of Statistical Planning and Inference
Volume103
Issue number1-2
DOIs
StatePublished - Apr 15 2002

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Cone order monotonicity
  • Maximum likelihood estimators
  • Order restricted inference
  • Preservation of order
  • Projections

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