Skip to main content
SpringerLink
Log in

Finite alogorithms for robust linear regression

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

In this paper Hubert's M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may be useful also in solving thel 1 problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. I. Clark:The mathematical structure of Huber's M-estimator. SIAM J. Sci. Stat. Comp. 6 (1985), 209–219.

    Google Scholar 

  2. D. I. Clark and M. R. Osborne:Finite algorithms for Huber's M-estimator. SIAM J. Sci. Stat. Comp. 7 (1986), 72–85.

    Google Scholar 

  3. J. Dongarra, J. Du Croz, S. Hammarling, and R. Hansen:An extended set of Fortran Basic Linear Algebra Subprograms. ACM Trans. Math. Soft. 14 (1988), 1–17.

    Google Scholar 

  4. R. Dutter:Numerical solution of robust regression problems: computational aspects, a comparison. J. Statist. Comput. Simul. 5 (1977), 207–238.

    Google Scholar 

  5. H. Ekblom:A new algorithm for the Huber estimator in linear models. BIT 28 (1988), 123–132.

    Google Scholar 

  6. P. Huber:Robust estimation of a location parameter. Ann Math. Stat. 35 (1964), 73–101.

    Google Scholar 

  7. P. Huber:Robust Statistics. John Wiley, New York, 1981.

    Google Scholar 

  8. P. Huber and R. Dutter:Numerical solution of robust regression problems. COMPSTAT 1974 Proc. Symposium on Computational Statistics. G. Brushmann (ed). Physike Verlag, Berlin. 165–172.

    Google Scholar 

  9. H. B. Nielsen:LHUBER, a Fortran 77 function for linear Huber estimation. Report NI 89-03, Institute for Numerical Analysis, Techn. Univ. of Denmark. 1989.

  10. W. H. Press, B. P. Flannery, S. A. Teukolsk, and W. T. Vetterling:Numerical Recipes. Cambridge University Press, Cambridge, 1986.

    Google Scholar 

  11. D. F. Shanno and D. M. Rocke:Numerical methods for robust regression: linear models. SIAM J. Sci. Stat. Comp. 7 (1986), 86–97.

    Google Scholar 

  12. G. A. Watson:Approximation Theory and Numerical Methods. John Wiley, New York, 1980.

    Google Scholar 

  13. J. H. Wilkinson:Rounding Errors in Algebraic Processes. H.M.S.O., London, 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Numerical Analysis, Technical University of Denmark, 2800, Lyngby, Denmark

    Kaj Madsen & Hans Bruun Nielsen

Authors
  1. Kaj Madsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans Bruun Nielsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Madsen, K., Nielsen, H.B. Finite alogorithms for robust linear regression. BIT 30, 682–699 (1990). https://doi.org/10.1007/BF01933216

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933216

AMS (MOS) subjects classifications

Keywords

Search

Navigation