Outlier detection in regression using an iterated one-step approximation to the Huber-skip estimator
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Outlier detection in regression using an iterated one-step approximation to the Huber-skip estimator. / Johansen, Søren; Nielsen, Bent.
I: Econometrics, Bind 1, Nr. 1, 2013, s. 53-70.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Outlier detection in regression using an iterated one-step approximation to the Huber-skip estimator
AU - Johansen, Søren
AU - Nielsen, Bent
PY - 2013
Y1 - 2013
N2 - In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip
AB - In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip
KW - Faculty of Social Sciences
KW - Huber-skip
KW - iteration
KW - one-step M-estimators
KW - unit roots
U2 - 10.3390/econometrics1010053
DO - 10.3390/econometrics1010053
M3 - Journal article
VL - 1
SP - 53
EP - 70
JO - Econometrics
JF - Econometrics
SN - 2225-1146
IS - 1
ER -
ID: 44881283