Generalized confidence intervals for proportions of total variance in mixed linear models

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Abstract

Exact confidence intervals for a proportion of total variance, based on pivotal quantities, only exist for mixed linear models having two variance components. Generalized confidence intervals (GCIs) introduced by Weerahandi [1993. Generalized confidence intervals (Corr: 94V89 p726). J. Am. Statist. Assoc. 88, 899-905] are based on generalized pivotal quantities (GPQs) and can be constructed for a much wider range of models. In this paper, the author investigates the coverage probabilities, as well as the utility of GCIs, for a proportion of total variance in mixed linear models having more than two variance components. Particular attention is given to the formation of GPQs and GCIs in mixed linear models having three variance components in situations where the data exhibit complete balance, partial balance, and partial imbalance. The GCI procedure is quite general and provides a useful method to construct confidence intervals in a variety of applications.

Original languageEnglish (US)
Pages (from-to)2394-2404
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume137
Issue number7
DOIs
StatePublished - Jul 1 2007

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Keywords

  • Coverage probability
  • Crossed and nested designs
  • Variance components

ASJC Scopus subject areas

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

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