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Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator

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  • Søren Johansen

    (Department of Economics, University of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen, Denmark
    CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4,8210 Aarhus, Denmark)

  • Bent Nielsen

    (Department of Economics, University of Oxford & Nuffield College, OX1 1NF, Oxford, UK)

Abstract

In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip.

Suggested Citation

  • Søren Johansen & Bent Nielsen, 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator," Econometrics, MDPI, vol. 1(1), pages 1-18, May.
    • Handle: RePEc:gam:jecnmx:v:1:y:2013:i:1:p:53-70:d:25659
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    References listed on IDEAS

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    1. repec:bot:quadip:118 is not listed on IDEAS
    2. David F. Hendry & Hans-Martin Krolzig, 2005. "The Properties of Automatic "GETS" Modelling," Economic Journal, Royal Economic Society, vol. 115(502), pages 32-61, March.
    3. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    4. Cavaliere, Giuseppe & Georgiev, Iliyan, 2013. "Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1162-1195, December.
    5. Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," Discussion Papers 13-01, University of Copenhagen. Department of Economics.
    6. Bent Nielsen & Soren Johansen, 2010. "Discussion of The Forward Search: Theory and Data Analysis," Economics Series Working Papers 2010-W02, University of Oxford, Department of Economics.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. From My Reading List...........
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-08-27 02:03:00

    Citations

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    Cited by:

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    5. Hendry, David F. & Pretis, Felix, 2023. "Analysing differences between scenarios," International Journal of Forecasting, Elsevier, vol. 39(2), pages 754-771.
    6. Ericsson, Neil R., 2017. "Interpreting estimates of forecast bias," International Journal of Forecasting, Elsevier, vol. 33(2), pages 563-568.
    7. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    8. Felix Pretis & Michael Mann & Robert Kaufmann, 2015. "Testing competing models of the temperature hiatus: assessing the effects of conditioning variables and temporal uncertainties through sample-wide break detection," Climatic Change, Springer, vol. 131(4), pages 705-718, August.
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    10. Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry & Felix Pretis, 2015. "Detecting Location Shifts during Model Selection by Step-Indicator Saturation," Econometrics, MDPI, vol. 3(2), pages 1-25, April.

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