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On various confidence intervals post-model-selection

Author

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  • Leeb, Hannes
  • Pötscher, Benedikt M.
  • Ewald, Karl

Abstract

We compare several confidence intervals after model selection in the setting recently studied by Berk et al. (2013), where the goal is to cover not the true parameter but a certain non-standard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the `naive' confidence interval, which is constructed as if the selected model were correct and fixed a-priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.

Suggested Citation

  • Leeb, Hannes & Pötscher, Benedikt M. & Ewald, Karl, 2014. "On various confidence intervals post-model-selection," MPRA Paper 58326, University Library of Munich, Germany, revised 2014.
    • Handle: RePEc:pra:mprapa:58326
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    References listed on IDEAS

    as
    1. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    2. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
    3. Pötscher, Benedikt M. & Schneider, Ulrike, 2008. "Confidence sets based on penalized maximum likelihood estimators," MPRA Paper 9062, University Library of Munich, Germany.
    4. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    5. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(4), pages 463-482, August.
    6. Hannes Leeb, 2006. "The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations," Papers math/0611186, arXiv.org.
    7. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    8. Pötscher, Benedikt M. & Schneider, Ulrike, 2011. "Distributional results for thresholding estimators in high-dimensional Gaussian regression models," MPRA Paper 31882, University Library of Munich, Germany.
    9. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    10. Kabaila, Paul & Leeb, Hannes, 2006. "On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 619-629, June.
    11. Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.
    12. Leeb, Hannes & Pötscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(1), pages 100-142, February.
    13. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(2), pages 163-185, June.
    14. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, May.
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    Keywords

    Confidence intervals; model selection;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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