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On the inefficiency of the restricted maximum likelihood

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  • Nicholas T. Longford

Abstract

type="main" xml:id="stan12055-abs-0001"> The restricted maximum likelihood is preferred by many to the full maximum likelihood for estimation with variance component and other random coefficient models, because the variance estimator is unbiased. It is shown that this unbiasedness is accompanied in some balanced designs by an inflation of the mean squared error. An estimator of the cluster-level variance that is uniformly more efficient than the full maximum likelihood is derived. Estimators of the variance ratio are also studied.

Suggested Citation

  • Nicholas T. Longford, 2015. "On the inefficiency of the restricted maximum likelihood," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 171-196, May.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:2:p:171-196
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    References listed on IDEAS

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    1. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    2. Stavros Kourouklis, 2012. "A New Estimator of the Variance Based on Minimizing Mean Squared Error," The American Statistician, Taylor & Francis Journals, vol. 66(4), pages 234-236, November.
    3. Kubokawa, T., 1995. "Estimation of Variance Components in Mixed Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 210-236, May.
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    1. Longford Nicholas T., 2021. "Unreported standard errors in meta-analysis," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 1-17, December.
    2. Nicholas T. Longford, 2021. "Unreported standard errors in meta-analysis," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 1-17, December.

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