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Compstat pp 217–222Cite as

Algorithms for Non-Linear Huber Estimation

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Abstract

In the non-linear least squares problem we minimize

$$ \frac{1}{2}{\rm{ }}\mathop \sum \limits_{j = 1}^m {\rm{ }}{{\rm{f}}_{\rm{j}}}{{\rm{ }}^2}(x) $$
(1.1)

where f1,..., fm is a set of non-linear smooth functions ℜn → ℜ and x is an n-vector of “parameters”.

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References

  1. J.E. Dennis, Non-linear Least Squares and Equations, In State of the Art in Numerical Analysis, (ed. D.A.H. Jacobs), Academic Press, 269–312, 1977.

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  6. F.R. Hampel, E. Ronchetti, P. Rousseeuw, W. Stahel, Robust Statistics: the infinitesimal approach, John Wiley, New York, 1986.

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  9. K. Madsen and H.B. Nielsen, Finite algorithms for robust linear regression, DCAMM Report No. 395, Technical Univ. of Denmark, 1989. Accepted for publication in BIT.

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  10. D. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, SLAM J. Appl. Math. (1963).

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Author information

Authors and Affiliations

  1. Luleå, Sweden

    H. Ekblom

  2. Lyngby, Denmark

    K. Madsen

Authors
  1. H. Ekblom
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  2. K. Madsen
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Editor information

Editors and Affiliations

  1. University of Zagreb, Engelsova bb, 41000, Zagreb, Yugoslavia

    Konstantin Momirović  & Vesna Mildner MA  & 

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© 1990 Physica-Verlag Heidelberg

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Cite this paper

Ekblom, H., Madsen, K. (1990). Algorithms for Non-Linear Huber Estimation. In: Momirović, K., Mildner, V. (eds) Compstat. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-50096-1_34

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  • DOI: https://doi.org/10.1007/978-3-642-50096-1_34

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0475-1

  • Online ISBN: 978-3-642-50096-1

  • eBook Packages: Springer Book Archive

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