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Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood

Author

Listed:
  • Vanessa Berenguer Rico
  • Bent Nielsen
  • Søren Johansen

Abstract

The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h; a sub-sample of h 'good' observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be h 1/2 consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.

Suggested Citation

  • Vanessa Berenguer Rico & Bent Nielsen & Søren Johansen, 2019. "Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood," Economics Series Working Papers 879, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:879
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Jurgen A. Doornik, 2016. "An Example of Instability: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 357-359, June.
    3. Vanessa Berenguer Rico & Ines Wilms, 2018. "White heteroscedasticty testing after outlier removal," Economics Series Working Papers 853, University of Oxford, Department of Economics.
    4. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals," CREATES Research Papers 2019-12, Department of Economics and Business Economics, Aarhus University.
    5. Rousseeuw, Peter & Perrotta, Domenico & Riani, Marco & Hubert, Mia, 2019. "Robust Monitoring of Time Series with Application to Fraud Detection," Econometrics and Statistics, Elsevier, vol. 9(C), pages 108-121.
    6. Jurgen A. Doornik & David F. Hendry, 2016. "Outliers and Model Selection: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 360-365, June.
    7. Vanessa Berenguer Rico & Bent Nielsen, 2017. "Marked and Weighted Empirical Processes of Residuals with Applications to Robust Regressions," Economics Series Working Papers 841, University of Oxford, Department of Economics.
    8. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.
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    More about this item

    Keywords

    Chebychev estimator; LMS; Uniform distribution; Least squares estimator; LTS; Normal distribution; Regression; Robust statistics;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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