Statistics and Computing

, Volume 27, Issue 6, pp 1655–1675 | Cite as

Fast and robust estimators of variance components in the nested error model

  • B. Pérez
  • I. MolinaEmail author
  • A. Thieler
  • R. Fried
  • D. Peña


Usual fitting methods for the nested error linear regression model are known to be very sensitive to the effect of even a single outlier. Robust approaches for the unbalanced nested error model with proved robustness and efficiency properties, such as M-estimators, are typically obtained through iterative algorithms. These algorithms are often computationally intensive and require robust estimates of the same parameters to start the algorithms, but so far no robust starting values have been proposed for this model. This paper proposes computationally fast robust estimators for the variance components under an unbalanced nested error model, based on a simple robustification of the fitting-of-constants method or Henderson method III. These estimators can be used as starting values for other iterative methods. Our simulations show that they are highly robust to various types of contamination of different magnitude.


Clustered data Linear mixed model Random effects Robust fitting Variance estimation 



Supported by the Spanish grants MTM2015-69638-R, MTM2012-37077-C02-01 and SEJ2007-64500, and by the European project num. 217565-FP7-SSH-2007-1

Supplementary material

11222_2016_9710_MOESM1_ESM.pdf (270 kb)
Supplementary material 1 (pdf 269 KB)


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Quantitative MethodsUniversity of PannoniaVeszprémHungary
  2. 2.Department of StatisticsUniversidad Carlos III de MadridGetafe (Madrid)Spain
  3. 3.Department of StatisticsTU Dortmund UniversityDortmundGermany

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