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Robust Model Selection and M-Estimation


  • Machado, José A.F.


This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining M -estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general M -estimators is also studied. The paper concludes with a Monte Carlo study of the finite sample behavior of the SIC for different specifications of the sample objective function.

Suggested Citation

  • Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(03), pages 478-493, June.
  • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:478-493_00

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    References listed on IDEAS

    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
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    3. Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
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    5. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
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    Cited by:

    1. Rockey, James & Temple, Jonathan, 2016. "Growth econometrics for agnostics and true believers," European Economic Review, Elsevier, vol. 81(C), pages 86-102.
    2. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    3. Fritsch, Markus & Haupt, Harry & Ng, Pin T., 2016. "Urban house price surfaces near a World Heritage Site: Modeling conditional price and spatial heterogeneity," Regional Science and Urban Economics, Elsevier, vol. 60(C), pages 260-275.
    4. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    5. Mao, Guangyu, 2015. "Model selection of M-estimation models using least squares approximation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 238-243.
    6. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    7. La Vecchia, Davide & Camponovo, Lorenzo & Ferrari, Davide, 2015. "Robust heart rate variability analysis by generalized entropy minimization," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 137-151.
    8. Mao, Guangyu, 2013. "Model selection for regression with heteroskedastic and autocorrelated errors," Economics Letters, Elsevier, vol. 118(3), pages 497-501.
    9. Xu, Qifa & Niu, Xufeng & Jiang, Cuixia & Huang, Xue, 2015. "The Phillips curve in the US: A nonlinear quantile regression approach," Economic Modelling, Elsevier, vol. 49(C), pages 186-197.
    10. Bera Anil K. & Galvao Antonio F. & Montes-Rojas Gabriel V. & Park Sung Y., 2016. "Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 79-101, January.
    11. Giuzio, Margherita & Ferrari, Davide & Paterlini, Sandra, 2016. "Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization," European Journal of Operational Research, Elsevier, vol. 250(1), pages 251-261.
    12. Bera, A. K. & Galvao Jr, A. F. & Montes-Rojas, G. & Park, S. Y., 2010. "Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression," Working Papers 10/08, Department of Economics, City University London.
    13. Huiyu Huang & Tae-Hwy Lee, 2013. "Forecasting Value-at-Risk Using High-Frequency Information," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 1-14, June.
    14. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    15. Arie Preminger & Shinichi Sakata, 2007. "A model selection method for S-estimation," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 294-319, July.
    16. repec:wyi:journl:002126 is not listed on IDEAS
    17. repec:wyi:journl:002094 is not listed on IDEAS
    18. Baierl, Andreas & Futschik, Andreas & Bogdan, Malgorzata & Biecek, Przemyslaw, 2007. "Locating multiple interacting quantitative trait loci using robust model selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6423-6434, August.

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