Discussiones Mathematicae Probability and Statistics 20(1) (2000) 85-95

ASYMPTOTIC NORMALITY AND EFFICIENCY OF VARIANCE COMPONENTS ESTIMATORS WITH HIGH BREAKDOWN POINTS

Christine H. Müller

Georg-August-University Göttingen, Institute of Mathematical Stochastics
Lotzestr. 13, 37083 Göttingen, Germany

e-mail:
chmuelle@math.unigoettingen.de

Abstract

For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw andCroux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of the maximum likelihood estimators.

Keywords: variance component model, robust estimation, Q estimator, asymptotic normality.

1991 Mathematics Subject Classification: Primary 62F12; Secondary 62F35.

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Received 27 November 1998
Revised 3 August 1999