Template-type: ReDIF-Paper 1.0
Author-Name: Vanessa Berenguer-Rico
Author-Workplace-Name: Department of Economics and Mansfield College, University of Oxford
Author-Email: vanessa.berenguer-rico@economics.ox.ac.uk
Author-Name: Søren Johansen
Author-Workplace-Name: University of Copenhagen and CREATES and Aarhus University
Author-Email: soren.johansen@econ.ku.dk
Author-Name: Bent Nielsen
Author-Workplace-Name: Department of Economics and Nuffield College, University of Oxford
Author-Email: bent.nielsen@economics.ox.ac.uk
Title: Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals
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.
Classification-JEL: C01, C22
Keywords: 1-step Huber skip, Asymptotic theory, Empirical processes, Gauge, Marked and Weighted Empirical processes, Non-stationarity, Robust Statistics, Stationarity
Length: 22 pages
Creation-Date: 2019-05-24
Number: 2019-W04
File-URL: https://www.nuffield.ox.ac.uk/economics/Papers/2019/2019W04_EP_VSB_consis_24may2019.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:1904