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Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator
Department of Economics, University of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen, Denmark
CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4,8210 Aarhus, Denmark
Department of Economics, University of Oxford & Nuffield College, OX1 1NF, Oxford, UK
* Author to whom correspondence should be addressed.
Received: 28 January 2013; in revised form: 3 April 2013 / Accepted: 3 April 2013 / Published: 13 May 2013
Abstract: In regression we can delete outliers based upon a preliminary estimator and re-estimate 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.
Keywords: Huber-skip; iteration; one-step M-estimators; unit roots
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Johansen, S.; Nielsen, B. Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator. Econometrics 2013, 1, 53-70.
Johansen S, Nielsen B. Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator. Econometrics. 2013; 1(1):53-70.
Johansen, Søren; Nielsen, Bent. 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator." Econometrics 1, no. 1: 53-70.