Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

22 Pages Posted: 18 Jun 2019

See all articles by Vanessa Berenguer-Rico

Vanessa Berenguer-Rico

University of Barcelona - Department of Econometrics

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Bent Nielsen

University of Oxford - Nuffield Department of Medicine

Date Written: May 24, 2019

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 initial 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: Huber skip, Asymptotic theory, Empirical processes, Gauge, Marked and Weighted Empirical processes, Non-stationarity, Robust Statistics, Stationarity

JEL Classification: C01, C22

Suggested Citation

Berenguer-Rico, Vanessa and Johansen, Soren and Nielsen, Bent, Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals (May 24, 2019). Available at SSRN: https://ssrn.com/abstract=3400724 or http://dx.doi.org/10.2139/ssrn.3400724

Vanessa Berenguer-Rico

University of Barcelona - Department of Econometrics ( email )

Av. Diagonal 690
Barcelona, E-08034
Spain

Soren Johansen

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Bent Nielsen (Contact Author)

University of Oxford - Nuffield Department of Medicine ( email )

New Road
Oxford, OX1 1NF
United Kingdom

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