Next Article in Journal
Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments
Previous Article in Journal
Constructing U.K. Core Inflation
Econometrics 2013, 1(1), 53-70; doi:10.3390/econometrics1010053

Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator

1 Department of Economics, University of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen, Denmark 2 CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4,8210 Aarhus, Denmark 3 Department of Economics, University of Oxford & Nuffield College, OX1 1NF, Oxford, UK
* Author to whom correspondence should be addressed.
Received: 28 January 2013 / Revised: 3 April 2013 / Accepted: 3 April 2013 / Published: 13 May 2013
View Full-Text   |   Download PDF [315 KB, uploaded 13 May 2013]


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 Huber-skip; iteration; one-step M-estimators; unit roots
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

Johansen, S.; Nielsen, B. Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator. Econometrics 2013, 1, 53-70.

View more citation formats

Related Articles

Article Metrics


[Return to top]
Econometrics EISSN 2225-1146 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert