Modified p-value of two-sided test for normal distribution with restricted parameter space

Hsiuying Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This article proposes a modified p -value for the two-sided test of the location of the normal distribution when the parameter space is restricted. A commonly used test for the two-sided test of the normal distribution is the uniformly most powerful unbiased (UMPU) test, which is also the likelihood ratio test. The p -value of the test is used as evidence against the null hypothesis. Note that the usual p -value does not depend on the parameter space but only on the observation and the assumption of the null hypothesis. When the parameter space is known to be restricted, the usual p -value cannot sufficiently utilize this information to make a more accurate decision. In this paper, a modified p -value (also called the rp -value) dependent on the parameter space is proposed, and the test derived from the modified p-value is also shown to be the UMPU test.

Original languageEnglish
Pages (from-to)1361-1374
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume35
Issue number8
DOIs
StatePublished - 1 Aug 2006

Keywords

  • p-Value
  • rp-Value
  • Two-sided test
  • Uniformly most powerful unbiased test

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