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Valid confidence intervals for post-model-selection predictors

Author

Listed:
  • Bachoc, Francois
  • Leeb, Hannes
  • Pötscher, Benedikt M.

Abstract

We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to post-model-selection predictors.

Suggested Citation

  • Bachoc, Francois & Leeb, Hannes & Pötscher, Benedikt M., 2014. "Valid confidence intervals for post-model-selection predictors," MPRA Paper 60643, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:60643
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    File URL: https://mpra.ub.uni-muenchen.de/76453/9/MPRA_paper_76453.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Leeb, Hannes & Pötscher, Benedikt M., 2012. "Testing in the Presence of Nuisance Parameters: Some Comments on Tests Post-Model-Selection and Random Critical Values," MPRA Paper 41459, University Library of Munich, Germany.
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    Cited by:

    1. Isaiah Andrews & Toru Kitagawa & Adam McCloskey, 2024. "Inference on Winners," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 139(1), pages 305-358.

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    More about this item

    Keywords

    Inference post-model-selection; confidence intervals; optimal post-model-selection predictors; non-standard targets; linear regression;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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