A Model Selection Method for S-Estimation

CORE Discussion Paper No. 2005/73

41 Pages Posted: 28 Feb 2006

See all articles by Arie Preminger

Arie Preminger

University of Haifa - Department of Economics; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Shinichi Sakata

University of British Columbia (UBC)

Date Written: November 2005

Abstract

In least squares, least absolute deviations, and even generalized M-estimation, outlying observations sometimes strongly influence the estimation result, masking an important and interesting relationship existing in the majority of observations. The S-estimators are a class of estimators that overcome this difficulty by smoothly downweighting outliers in fitting regression functions to data.

In this paper, we propose a method of model selection suitable in S-estimation. The proposed method chooses a model to minimize a criterion named the penalized S-scale criterion (PSC), which is decreasing in the sample S-scale of fitted residuals and increasing in the number of parameters. We study the large sample behavior of the PSC in nonlinear regression with dependent, heterogeneous data, to establish sets of conditions sufficient for the PSC to consistently select the model with the best fitting performance in terms of the population S-scale, and the one with the minimum number of parameters if there are multiple best performers. Our analysis allows for partial unidentifiability, which is often a practically important possibility when selecting one among nonlinear regression models. We offer two examples to demonstrate how our large sample results could be applied in practice. We also conduct Monte Carlo simulations to verify that the PSC performs as our large sample theory indicates, and assess the reliability of the PSC method in comparison with the familiar Akaike and Schwarz information criteria.

Keywords: Robust model selection, partial identification, law of the iterated logarithm

JEL Classification: C22, C52

Suggested Citation

Preminger, Arie and Sakata, Shinichi, A Model Selection Method for S-Estimation (November 2005). CORE Discussion Paper No. 2005/73, Available at SSRN: https://ssrn.com/abstract=885926 or http://dx.doi.org/10.2139/ssrn.885926

Arie Preminger

University of Haifa - Department of Economics ( email )

Haifa 31905
Israel

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Shinichi Sakata (Contact Author)

University of British Columbia (UBC) ( email )

Department of Economics
997-1873 East Mall
Vancouver, BC V6T 1Z4
Canada
(604) 822-5360 (Phone)
(604) 822-5915 (Fax)

HOME PAGE: http://www.econ.ubc.ca/ssakata/public_html/

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