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Asymptotic Behaviour of One-Step-M-Estimators in Contaminated Non-Linear Models

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Asymptotic Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

Extending the approach of Bickel (1975, 1981, 1984) and Rieder (1985, 1987) the asymptotic behaviour of one-step-M-estimators for 0 is investigated for nonlinear models Y(t) = μ(θ, t) + Z(t) where μ is a non-linear function in θ and the errors Z(t) may have different contaminated normal distributions for different experimental conditions t. These models are also called conditionally contaminated non-linear models. For these models it is shown that the one-step-M-estimators have an asymptotic bias which depends on θ as the asymptotic covariance matrix depends on θ. Using the results of Kurotschka and Müller (1992) and Müller (1992a) locally optimal robust one-step-M-estimators and corresponding optimal designs are derived by minimizing the trace of the asymptotic covariance matrix under the side condition that the asymptotic bias is bounded by some bias bound. The locally optimal solutions are appropriate to efficiency comparisons.

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Author information

Authors and Affiliations

  1. 1. Mathematisches Institut, Freie Universität Berlin, Arnimallee 2-6, D-14195, Berlin-Dahlem, France

    Christine H. Müller

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  1. Christine H. Müller
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Editor information

Editors and Affiliations

  1. Department of Probability and Mathematical Statistics, Charles University, Sokolovská 83, CZ-186 00, Praha 8, Czech Republic

    Petr Mandl  & Marie Hušková  & 

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© 1994 Springer-Verlag Berlin Heidelberg

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Müller, C.H. (1994). Asymptotic Behaviour of One-Step-M-Estimators in Contaminated Non-Linear Models. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_34

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  • DOI: https://doi.org/10.1007/978-3-642-57984-4_34

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0770-7

  • Online ISBN: 978-3-642-57984-4

  • eBook Packages: Springer Book Archive

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