Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals

May 2019 | 871

Authors: Vanessa Berenguer Rico, Bent Nielsen Søren Johansen

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.

JEL Codes: C01, C22

Keywords: 1-step Huber skip, Asymptotic theory, Empirical processes, Gauge, Marked and Weighted Empirical processes, Non-stationarity, Robust Statistics, Sta-tionarity

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