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A model selection method for S-estimation


  • 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.

Suggested Citation

  • PREMINGER, Arie & SAKATA, Shinichi, 2005. "A model selection method for S-estimation," CORE Discussion Papers 2005073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2005073

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    References listed on IDEAS

    1. 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.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
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    11. 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.
    12. 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.
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    18. 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.
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    Cited by:

    1. Preminger, Arie & Franck, Raphael, 2007. "Forecasting exchange rates: A robust regression approach," International Journal of Forecasting, Elsevier, vol. 23(1), pages 71-84.

    More about this item


    robust model selection; partial identification; law of the iterated logarithm;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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