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Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

Author

Listed:
  • Vanessa Berenguer-Rico

    (Department of Economics, University of Oxford)

  • Soeren Johansen

    (Department of Economics, University of Copenhagen, Denmark)

  • Bent Nielsen

    (Department of Economics, University of Oxford)

Abstract

A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker sufficient conditions for uniform consistency are derived. The theory allows for a wide variety of regressors and error distributions. We apply the theory to 1-step Huber-skip estimators. These estimators describe the widespread practice of removing outlying observations from an intial estimation of the model of interest and updating the estimation in a second step by applying least squares to the selected observations. Two results are presented. First, we give new and weaker conditions for consistency of the estimators. Second, we analyze the gauge, which is the rate of false detection of outliers, and which can be used to decide the cut-off in the rule for selecting outliers.

Suggested Citation

  • Vanessa Berenguer-Rico & Soeren Johansen & Bent Nielsen, 2019. "Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals," Discussion Papers 19-09, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1909
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    Cited by:

    1. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood," CREATES Research Papers 2019-15, Department of Economics and Business Economics, Aarhus University.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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