Two-stage Huber estimation

Tae Hwan Kim; Christophe Muller

doi:10.1016/j.jspi.2006.01.007

Two-stage Huber estimation

Tae Hwan Kim, Christophe Muller

Department of Economics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.

Original language	English
Pages (from-to)	405-418
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	137
Issue number	2
DOIs	https://doi.org/10.1016/j.jspi.2006.01.007
Publication status	Published - 2007 Feb 1

Bibliographical note

Funding Information:
This research has been supported under the British Academy Award No. 30,649. Tae-Hwan Kim is grateful to the College of Business and Economics of Yonsei University for financial support under the project code 2005-1-0244 and the second author is grateful for the financial support by Spanish Ministry of Sciences and Technology. Project No. BEC2002-03097 and by the Instituto Valenciano de Investigaciones Economicas. We thank participants in a seminar in Alicante and two referees for their useful comments. Usual disclaimers apply.

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.",

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