More powerful tests for the sign testing problem

Khalil G. Saikali, Roger L. Berger

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

For i = 1,..., p, let Xi1,..., Xini denote independent random samples from normal populations. The ith population has unknown mean μi and unknown variance σi2. We consider the sign testing problem of testing H0: μi ≤ ai, for some i=1,..., p, versus H1: μi > ai, for all i=1,..., p, where a1,..., ap are fixed constants. Here, H1 might represent p different standards that a product must meet before it is considered acceptable. For 0 < α < 1/2, we first derive the size-α likelihood ratio test (LRT) for this problem, and then we describe an intersection-union test (IUT) that is uniformly more powerful than the likelihood ratio test if the sample sizes are not all equal. For a more general model than the normal, we describe two intersection-union tests that maximize the size of the rejection region formed by intersection. Applying these tests to the normal problem yields two tests that are uniformly more powerful than both the LRT and IUT described above. A small power comparison of these tests is given.

Original languageEnglish (US)
Pages (from-to)187-205
Number of pages19
JournalJournal of Statistical Planning and Inference
Volume107
Issue number1-2
DOIs
StatePublished - Sep 1 2002

Keywords

  • Independence
  • Intersection-union test
  • Likelihood ratio test
  • Min test
  • Normal population
  • t distribution

ASJC Scopus subject areas

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

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