Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

Vanessa Berenguer-Rico (), Soren Johansen and Bent Nielsen ()
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Vanessa Berenguer-Rico: Department of Economics and Mansfield College, University of Oxford
Bent Nielsen: Department of Economics and Nuffield College, University of Oxford

No 2019-W04, Economics Papers from Economics Group, Nuffield College, University of Oxford

Abstract: A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker su¢ cient 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-o§ in the rule for selecting outliers.

Keywords: 1-step Huber skip; Asymptotic theory; Empirical processes; Gauge; Marked and Weighted Empirical processes; Non-stationarity; Robust Statistics; Stationarity (search for similar items in EconPapers)
JEL-codes: C01 C22 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2019-05-24
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals (2019)
Working Paper: Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals (2019)
Working Paper: Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals (2019)
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