Robust Parameter Estimation Based on Huber Estimator in Systems of Differential Equations

Conference paper

Abstract

The paper discusses the use of the Huber estimator for parameter estimation problems which are constrained by a system of ordinary differential equations. In particular, a local and global convergence analysis for the estimation with the Huber estimator is given. For comparison, numerical results are given for an estimation with this estimator and both l 1 estimation and the least squares approach for a parameter estimation problem for a chemical process.

Keywords

Line Search Strict Complementarity Parameter Estimation Problem Exact Penalty Function Partition Constant 
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References

  1. 1.
    Bock, H.G.: Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen. Bonner Mathematische Schriften, 183, Bonn (1987).Google Scholar
  2. 2.
    Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. Wiley, New York (1986)MATHGoogle Scholar
  3. 3.
    Huber, P.J.: Robust Statistics. Wiley, New York (1981)MATHCrossRefGoogle Scholar
  4. 4.
    Huber, P.J.: Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35, 73–101 (1964)MATHCrossRefGoogle Scholar
  5. 5.
    Ekblom, H., Madsen, K.: Algorithms for Non-linear Huber Estimation. BIT, 29, 60–76 (1989)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of MarburgMarburgGermany

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