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Finite alogorithms for robust linear regression

Finite alogorithms for robust linear regression

JournalBIT Numerical Mathematics
PublisherSpringer Netherlands
ISSN0006-3835 (Print) 1572-9125 (Online)
IssueVolume 30, Number 4 / December, 1990
CategoryPart II Numerical Mathematics
DOI10.1007/BF01933216
Pages682-699
Subject CollectionMathematics and Statistics
SpringerLink DateMonday, August 01, 2005
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Part II Numerical Mathematics

Finite alogorithms for robust linear regression

Kaj Madsen1 and Hans Bruun Nielsen1

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

Received: 15 September 1989  Revised: 15 April 1990  

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.

AMS (MOS) subjects classifications  62J05 - 65D10 - 65F20 - 65U05

Keywords  Robust regression - Huber estimator - Newton's method - Rank deficient problems

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Referenced by
10 newer articles

  1. Madsen, Kaj (1998) A Finite Continuation Algorithm for Bound Constrained Quadratic Programming. SIAM Journal on Optimization 9(1)
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  2. Madsen, Kaj (1993) A Finite Smoothing Algorithm for Linear $l_1 $ Estimation. SIAM Journal on Optimization 3(2)
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  3. Madsen, Kaj (1996) A New Finite Continuation Algorithm for Linear Programming. SIAM Journal on Optimization 6(3)
    [CrossRef]
  4. Mangasarian, O.L. (2000) Robust linear and support vector regression. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(9)
    [CrossRef]
  5. Ferguson, J. F. (2007) The 4D microgravity method for waterflood surveillance II — Gravity measurements for the Prudhoe Bay reservoir, Alaska. Geophysics 72(2)
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  6. Bo, Liefeng (2007) Recursive Finite Newton Algorithm for Support Vector Regression in the Primal. Neural Computation 19(4)
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  7. Edlund, Ove (1997) Linear M-estimation with bounded variables. Bit Numerical Mathematics 37(1)
    [CrossRef]
  8. Chen, B. (1998) On Newton's method for Huber's robust M-estimation problems in linear regression. Bit Numerical Mathematics 38(4)
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  9. Pinar, Mustafa C. (1998) A penalty continuation method for the ∓∞ solution of overdetermined linear systems. Bit Numerical Mathematics 38(1)
    [CrossRef]
  10. Wolke, Ralf (1992) Iteratively reweighted least squares: A comparison of several single step algorithms for linear models. BIT 32(3)
    [CrossRef]
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