Confidence intervals for the mean of a normal distribution with restricted parameter space

Hsiuying Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

For a normal distribution with known variance, the standard confidence interval of the location parameter is derived from the classical Neyman procedure. When the parameter space is known to be restricted, the standard confidence interval is arguably unsatisfactory. Recent articles have addressed this problem and proposed confidence intervals for the mean of a normal distribution where the parameter space is not less than zero. In this article, we propose a new confidence interval, rp interval, and derive the Bayesian credible interval and likelihood ratio interval for general restricted parameter space. We compare these intervals with the standard interval and the minimax interval. Simulation studies are undertaken to assess the performances of these confidence intervals.

Original languageEnglish
Pages (from-to)829-841
Number of pages13
JournalJournal of Statistical Computation and Simulation
Volume78
Issue number9
DOIs
StatePublished - 25 Sep 2008

Keywords

  • Bayesian credible interval
  • Coverage probability
  • Likelihood ratio interval
  • rp interval

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