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An Analysis of the Least Median of Squares Regression Problem

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Computational Statistics

Abstract

The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, it is replaced by an equivalent problem of minimizing the median of absolute residuals. A useful representation of the last problem is given to examine properties of the objective function and estimate the number of its local minima.

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References

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Author information

Authors and Affiliations

  1. St.Petersburg University, Bibliotechnaya sq.2, 198904, St.Petersburg, Petrodvorets, Russia

    Nikolai Krivulin (Faculty of Mathematics and Mechanics)

Authors
  1. Nikolai Krivulin
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Editor information

Editors and Affiliations

  1. Groupe de Statistique, University of Neuchâtel, Pierre-à-Mazel 7, CH-2000, Neuchâtel, Switzerland

    Yadolah Dodge (Professor of Statistics and Operations Research) (Professor of Statistics and Operations Research)

  2. Lancaster University, GB-Lancaster, LA1 4YE, Great Britain

    Joe Whittaker (Professor of Mathematics) (Professor of Mathematics)

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© 1992 Springer-Verlag Berlin Heidelberg

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Krivulin, N. (1992). An Analysis of the Least Median of Squares Regression Problem. In: Dodge, Y., Whittaker, J. (eds) Computational Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-26811-7_65

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  • DOI: https://doi.org/10.1007/978-3-662-26811-7_65

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-26813-1

  • Online ISBN: 978-3-662-26811-7

  • eBook Packages: Springer Book Archive

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