Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

Vanessa Berenguer-Rico (), Soren Johansen and Bent Nielsen ()
Additional contact information
Vanessa Berenguer-Rico: University of Oxford, Postal: Department of Economics, Mansfield College, Manor Road Building, Manor Road, Oxford OX1 3UQ, U.K.
Bent Nielsen: University of Oxford, Postal: Department of Economics, Nuffield College, Oxford, OX1 1NF, U.K.

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

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
Date: 2019-05-24
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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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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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2019-12

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