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A Robustified Version of Sliced Inverse Regression

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Statistics in Genetics and in the Environmental Sciences

Part of the book series: Trends in Mathematics ((TM))

Abstract

Sliced Inverse Regression (SIR) (Li, 1991) is a method for dimension reduction in (nonparametric) regression models, based on the idea of using the information contained in the inverse regression curve. In the various steps of the SIR procedure, classical statistical estimators are used. Thus, the resulting method is nonrobust, and an immediate possibility to robustify SIR is to replace the classical estimators by robust ones. This leads to procedures which maintain the clever estimation scheme of the original SIR method but can cope better with outliers in the regressor space. We present such robustified versions of SIR and compare them with the original procedure and among each other under different model assumptions.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Dortmund, Germany

    Ursula Gather, Torsten Hilker & Claudia Becker

Authors
  1. Ursula Gather
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  2. Torsten Hilker
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  3. Claudia Becker
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Editor information

Editors and Affiliations

  1. Department of Statistics, Temple University, Speakman Hall 006-00, Philadelphia, PA, 19122, USA

    Luisa Turrin Fernholz

  2. Department of Mathematics, Swiss Federal Institute of Technology, EPFL-DMA, 1015, Lausanne, Switzerland

    Stephan Morgenthaler

  3. Seminar for Statistics, Swiss Federal Institute of Technology, ETH-SOL, 8092, Zürich, Switzerland

    Werner Stahel

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© 2001 Springer Basel AG

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Gather, U., Hilker, T., Becker, C. (2001). A Robustified Version of Sliced Inverse Regression. In: Fernholz, L.T., Morgenthaler, S., Stahel, W. (eds) Statistics in Genetics and in the Environmental Sciences. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8326-9_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8326-9_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9518-7

  • Online ISBN: 978-3-0348-8326-9

  • eBook Packages: Springer Book Archive

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