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June 1998 Breakdown properties of location $M$-estimators
Guoying Li, Jian Zhang
Ann. Statist. 26(3): 1170-1189 (June 1998). DOI: 10.1214/aos/1024691093

Abstract

In this article, we consider the asymptotic behavior of three kinds of sample breakdown points. It is shown that for the location $M$-estimator with bounded objective function, both the addition sample breakdown point and the simplified replacement sample breakdown point strongly converge to the gross-error asymptotic breakdown point, whereas the replacement sample breakdown point strongly converges to a smaller value. In addition, it is proved that under some regularity conditions these sample breakdown points are asymptotically normal. The addition sample breakdown point has a smaller asymptotic variance than the simplified replacement sample breakdown point. For the commonly used redescending $M$-estimators of location, numerical results indicate that among the three kinds of sample breakdown points, the replacement sample breakdown point has the largest asymptotic variance.

Citation

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Guoying Li. Jian Zhang. "Breakdown properties of location $M$-estimators." Ann. Statist. 26 (3) 1170 - 1189, June 1998. https://doi.org/10.1214/aos/1024691093

Information

Published: June 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62031
MathSciNet: MR1635381
Digital Object Identifier: 10.1214/aos/1024691093

Subjects:
Primary: 62F35

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 3 • June 1998
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