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A new algorithm for the huber estimator in linear models

  • Part II Numerical Mathematics
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Abstract

This paper considers algorithms for solving the linear robust regression problem by minimizing the Huber function. In the computational methods for this problem used so far, the scale estimate is adjusted separately. The new algorithm, based on Newton's method, treats both the scale and the location parameters as independent variables. The special form of the Hessian allows for an efficient updating scheme.

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References

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

    Google Scholar 

  2. J. J. Dongarra et al.,LINPACK Users Guide, SIAM Publications, Philadelphia, 1979.

    Google Scholar 

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

    Google Scholar 

  4. H. Ekblom,Programs for the Huber estimator in linear models, Dept. of Math. 1985–5, Luleå University, Sweden.

  5. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw and W. A. Stahel,Robust Statistics: The Approach Based on Influence Functions, John Wiley, New York, 1986.

    Google Scholar 

  6. P. Huber,Robust Statistics, John Wiley, New York, 1981.

    Google Scholar 

  7. A. Marazzi,On the Numerical Solutions of Bounded Influence Regression Problems, in F. de Antonio, N. Laauro and A. Rizzi (eds.),COMPSTAT 86: Proceedings in Computational Statistics, Physica Verlag, Vienna, 1986.

    Google Scholar 

  8. Nag Reference Manual, Mark 10, NAG Central Office, Oxford, England, 1983.

  9. J. M. Ortega and W. C. Reinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, London and New York, 1970.

    Google Scholar 

  10. A. Ruhe and P. Å. Wedin,Algorithms for separable nonlinear least-squares problems, SIAM Review 22 (1980), 318–337.

    Google Scholar 

  11. D. F. Shanno and K. H. Phua,Research on Algorithm 500: Minimization of Unconstrained Multivariate Functions, ACM Trans. Math. Software 6 (1980), 618–622.

    Google Scholar 

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

    Google Scholar 

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Ekblom, H. A new algorithm for the huber estimator in linear models. BIT 28, 123–132 (1988). https://doi.org/10.1007/BF01934700

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  • DOI: https://doi.org/10.1007/BF01934700

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