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A model selection method for S-estimation

  • PREMINGER, Arie
  • SAKATA, Shinichi

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005073.

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Date of creation: 00 Nov 2005
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Handle: RePEc:cor:louvco:2005073
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  1. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
  2. Sibbertsen, Philipp, 1999. "S-estimation in the nonlinear regression model with long-memory error terms," Technical Reports 1999,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  3. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
  4. Filippo Altissimo & Valentina Corradi, 2002. "Bounds for inference with nuisance parameters present only under the alternative," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 494-519, 06.
  5. Balke, Nathan S & Fomby, Thomas B, 1994. "Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 181-200, April-Jun.
  6. Philipp Sibbertsen, 1999. "S-Estimation in the Linear Regression Model with Long-Memory Error Terms," Computing in Economics and Finance 1999 512, Society for Computational Economics.
  7. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  8. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(03), pages 478-493, June.
  9. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for Smooth Transition Nonlinearity in the Presence of Outliers," Econometric Institute Research Papers EI 9622-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  10. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  11. Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
  12. Baci, Sidika & Zaman, Asad, 1998. "Effects of skewness and kurtosis on model selection criteria," Economics Letters, Elsevier, vol. 59(1), pages 17-22, April.
  13. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
  14. Kapetanios, G., 1999. "Model Selection in Threshold Models," Cambridge Working Papers in Economics 9906, Faculty of Economics, University of Cambridge.
  15. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  16. Nishii, R., 1988. "Maximum likelihood principle and model selection when the true model is unspecified," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 392-403, November.
  17. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  18. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  19. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
  20. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
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