On drawbacks of least squares Lehmann–Scheffé estimation of variance components


Estimation of variance components is one of the basic problems in linear models with mixed effects, and a vast literature exists on the subject. Unfortunately, there are only few situations in which uniformly best estimators exist, which usually results into need of using an iterative estimation procedure. A new non-iterative method, called least squares Lehmann–Scheffé method, was proposed and its superiority over commonly accepted methods was claimed. Since there was no scientific response to these claims, we decided to analyze it thoroughly.

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The authors are grateful to prof. D. R. Cox, University of Oxford, for proposing the problem and for his comments on early drafts of the paper.

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Correspondence to Ivan Žežula.

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This work was supported by the Slovak Research and Development Agency under the contract no. APVV-17-0568.

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Žežula, I., Klein, D. On drawbacks of least squares Lehmann–Scheffé estimation of variance components. METRON (2021). https://doi.org/10.1007/s40300-021-00196-8

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  • Least squares estimation
  • Mixed linear model
  • Variance components