Improved large-sample confidence intervals for ratios of variance components in nonnormal distributions

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The confidence level of the usual interval for a ratio of variance components is contingent on normally distributed random variables. In this article we focus on confidence intervals for ratios of variance components in balanced one-way random effects models based on the large-sample properties of restricted maximum likelihood (REML) estimators. While this procedure does not require that the random variables be normally distributed, one must estimate a parameter that is a function of the kurtosis of the underlying distributions. Simulation results indicate that REML-based confidence interval methods outperform other well-known methods in the majority of the cases considered.

Original languageEnglish (US)
Pages (from-to)349-362
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume44
Issue number2
DOIs
StatePublished - Jan 17 2015

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Non-normal Distribution
Components of Variance
Confidence interval
Random variable
Restricted Maximum Likelihood Estimator
Restricted Maximum Likelihood
Interval Methods
Random Effects Model
Kurtosis
Confidence Level
Model-based
Interval
Estimate
Simulation

Keywords

  • Intraclass correlation coefficient
  • One-way random effects model
  • REML

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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abstract = "The confidence level of the usual interval for a ratio of variance components is contingent on normally distributed random variables. In this article we focus on confidence intervals for ratios of variance components in balanced one-way random effects models based on the large-sample properties of restricted maximum likelihood (REML) estimators. While this procedure does not require that the random variables be normally distributed, one must estimate a parameter that is a function of the kurtosis of the underlying distributions. Simulation results indicate that REML-based confidence interval methods outperform other well-known methods in the majority of the cases considered.",
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AB - The confidence level of the usual interval for a ratio of variance components is contingent on normally distributed random variables. In this article we focus on confidence intervals for ratios of variance components in balanced one-way random effects models based on the large-sample properties of restricted maximum likelihood (REML) estimators. While this procedure does not require that the random variables be normally distributed, one must estimate a parameter that is a function of the kurtosis of the underlying distributions. Simulation results indicate that REML-based confidence interval methods outperform other well-known methods in the majority of the cases considered.

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