Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals
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Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals. / Berenguer-Rico, Vanessa; Johansen, Søren; Nielsen, Bent.
2019.Research output: Working paper › Research
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TY - UNPB
T1 - Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals
AU - Berenguer-Rico, Vanessa
AU - Johansen, Søren
AU - Nielsen, Bent
PY - 2019/6/18
Y1 - 2019/6/18
N2 - 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.
AB - 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.
KW - Huber skip
KW - Asymptotic theory
KW - Empirical processes
KW - Gauge
KW - Marked and Weighted Empirical processes
KW - Non-stationarity
KW - Robust Statistics
KW - Stationarity
KW - Huber skip
KW - Asymptotic theory
KW - Empirical processes
KW - Gauge
KW - Marked and Weighted Empirical processes
KW - Non-stationarity
KW - Robust Statistics
KW - Stationarity
KW - C01
KW - C22
U2 - 10.2139/ssrn.3400724
DO - 10.2139/ssrn.3400724
M3 - Working paper
T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)
BT - Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals
ER -
ID: 248551209