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A procedure for robust fitting in nonlinear regression

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  • Hawkins, Douglas M.
  • Khan, Dost Muhammad

Abstract

Outliers present more of a challenge in nonlinear than in linear models. As in the linear case, methods based on full-sample fits are not guaranteed to give larger residuals on the outliers than on inliers, and so identification methods starting from full-sample fits may fail. In addition, the fitting involves iterative calculation rather than closed-form explicit solutions, with the potential problems of convergence to local rather than global optima. The elemental set method, which has long been a fundamental tool in high breakdown linear fitting, is well suited to some nonlinear regression problems, providing an effective way of fitting the nonlinear equation, and providing the capability of doing so even in the face of large numbers of severe outliers. We discuss the basic elemental set method, and the nonlinear FAST-LTS approach, and propose a hybrid method with elemental searches preceding concentration steps.

Suggested Citation

  • Hawkins, Douglas M. & Khan, Dost Muhammad, 2009. "A procedure for robust fitting in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4500-4507, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4500-4507
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    References listed on IDEAS

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    1. Olive, David J. & Hawkins, Douglas M., 2007. "Behavior of elemental sets in regression," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 621-624, March.
    2. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    3. Hawkins D. M. & Olive D. J., 2002. "Inconsistency of Resampling Algorithms for High-Breakdown Regression Estimators and a New Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 136-159, March.
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    Cited by:

    1. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.

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