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Breakdown Point and Computation of Trimmed Likelihood Estimators in Generalized Linear Models

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Developments in Robust Statistics

Summary

A review of the studies concerning the finite sample breakdown point (BP) of the trimmed likelihood (TL) and related estimators based on the d—fullness technique of Vandev (1993), and Vandev and Neykov (1998) is made. In particular, the BP of these estimators in the frame of the generalized linear models (GLMs) depends on the trimming proportion and the quantity N(X) introduced by Müller (1995). A faster iterative algorithm based on resampling techniques for derivation of the TLE is developed. Examples of real and artificial data in the context of grouped logistic and log-linear regression models are used to illustrate the properties of the TLE.

* The authors would like to thank the editors and the referees for their helpful comments. The research of N. Neykov was partialy funded by Deutsche Forschungsgemeinschaft while he was Visiting Fellow of the Inst. of Math. Stochastics, Univ. of Gottingen during May-June 1999. The Austrian Ministry of Science fully supported the participation of N. Neykov at the International Conference on Robust Statistics, 23-27 July 2001, Vorau, Austria. He acknowledged gratefully the financial supports.

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Author information

Authors and Affiliations

  1. National Inst. of Meteorology and Hydrology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    N. M. Neykov

  2. Dept. of Mathematics, Carl von Ossietzky University of Oldenburg, Germany

    C. H. Müller

Authors
  1. N. M. Neykov
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  2. C. H. Müller
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Editor information

Editors and Affiliations

  1. Institute of Statistics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna, 1040, Austria

    Rudolf Dutter  & Peter Filzmoser  & 

  2. Statistics Department, University of Dortmund, Dortmund, 44221, Germany

    Ursula Gather

  3. Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, Antwerp, 2610, Belgium

    Peter J. Rousseeuw

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© 2003 Springer-Verlag Berlin Heidelberg

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Neykov, N.M., Müller, C.H. (2003). Breakdown Point and Computation of Trimmed Likelihood Estimators in Generalized Linear Models. In: Dutter, R., Filzmoser, P., Gather, U., Rousseeuw, P.J. (eds) Developments in Robust Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57338-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-57338-5_24

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-642-63241-9

  • Online ISBN: 978-3-642-57338-5

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