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Biometrika 2001 88(2):353-366; doi:10.1093/biomet/88.2.353
© 2001 by Biometrika Trust
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Estimation of variance components with high breakdown point and high efficiency

Christine H.Müller1 and Steffen Uhlig2

1 Carl von Ossietzky University Oldenburg, Department 6 of Mathematics, Postfach 2503, D-26111 Oldenburg, Germanymueller{at}math.uni-oldenburg.de 2 Free University of Berlin, Institute of Statistics and Econometrics, Garystraße 21, D-14195 Berlin, Germany.uhlig{at}quodata.de

For the one-way random effects model three noniterative robust variance component estimators are investigated.For these estimators block breakdown points, measurement breakdown points and efficiency are derived. It is shown that the block breakdown points are approximating 50% and that the measurement breakdown points are not smaller than 25%. By deriving the asymptotic normal distribution of these estimators we show that two of the new estimators have an asymptotic efficiency greater than 82% and under certain circumstances up to 96%. Competing estimators have lower breakdown points and lower efficiencies. A simulation study shows that the high efficiency also appears for finite samples. The use of the estimators for interlaboratory tests is demonstrated in a practical example.

Key Words: Asymptotic normality; Breakdown point; Interlaboratory test; Q-estimator; Robust estimation; Variance component model

Received November 1998. Revised January 2000


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