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Linear Statistical Inference pp 88–98Cite as

Linear Statistical Inference Based on L-Estimators

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 35))

Abstract

Consider the linear model

$$\underset{\scriptscriptstyle\thicksim}{Y} = \underset{\scriptscriptstyle\thicksim}{X}\underset{\scriptscriptstyle\thicksim}{\beta} + \underset{\scriptscriptstyle\thicksim}{E},$$
((1.1))

where Y = (Y1,..., Yn)′ is a vector of independent observations, X is a known (n × p)-matrix, β = (β1,..., βp)′ is an unknown parameter and E = (E1,...,En)′ is a vector of independent errors identically distributed according to a distribution function (d.f.) F, which is either uknown or only partially known. We want to find an estimator for β which has high efficiency under normal d.f. F but which is able to endure mild perturbations from normality. The latter requirement is not satisfied by the classicial least-squares estimator (LSE).

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Author information

Authors and Affiliations

  1. Institute of Probability and Mathematical Statistics, Charles University, Prague, Czechoslovakia

    J. Jurečková

Authors
  1. J. Jurečková
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Editor information

Editors and Affiliations

  1. Mathematical Institute, Polish Academy of Sciences, ul. Kopernika 18, 51-617, Wroclaw, Poland

    T. Caliński  & W. Klonecki  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Jurečková, J. (1985). Linear Statistical Inference Based on L-Estimators. In: Caliński, T., Klonecki, W. (eds) Linear Statistical Inference. Lecture Notes in Statistics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7353-1_8

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  • DOI: https://doi.org/10.1007/978-1-4615-7353-1_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96255-9

  • Online ISBN: 978-1-4615-7353-1

  • eBook Packages: Springer Book Archive

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