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Robust Estimators of Location and Their Second-Order Asymptotic Relations

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A Celebration of Statistics

Abstract

Let X 1, …, X n be independent random variables, identically distributed according to the distribution function F(x — θ), where θ is the parameter to be estimated. F is generally unspecified; we only assume that F has a symmetric density f. Three broad classes of robust estimators of θ, these of M-estimators, L-estimators, and R-estimators, are first briefly described. Denoting these estimators M n, L n, and R n, respectively, we give sufficient conditions under which these estimators are asymptotically equivalent in probability, i.e., \(\sqrt n (M_n - L_n )\xrightarrow{p}0\), etc., as n → ∞. These relations are supplemented by the rates of convergence in most cases.

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Authors
  1. Jana Jurečková
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Editors and Affiliations

  1. Imperial College of Science and Technology, SW7 2BZ, London, England

    Anthony C. Atkinson

  2. Carnegie-Mellon University, 15213, Pittsburgh, Pennsylvania, USA

    Stephen E. Fienberg

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© 1985 Springer-Verlag New York Inc.

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Jurečková, J. (1985). Robust Estimators of Location and Their Second-Order Asymptotic Relations. In: Atkinson, A.C., Fienberg, S.E. (eds) A Celebration of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8560-8_16

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  • DOI: https://doi.org/10.1007/978-1-4613-8560-8_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8562-2

  • Online ISBN: 978-1-4613-8560-8

  • eBook Packages: Springer Book Archive

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