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On the Length of Post-Model-Selection Confidence Intervals Conditional on Polyhedral Constraints

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  • Danijel Kivaranovic
  • Hannes Leeb

Abstract

Valid inference after model selection is currently a very active area of research. The polyhedral method, introduced in an article by Lee et al., allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the length of these intervals. For one of these confidence intervals, which is easier to compute, we find that its expected length is always infinite. For the other of these confidence intervals, whose computation is more demanding, we give a necessary and sufficient condition for its expected length to be infinite. In simulations, we find that this sufficient condition is typically satisfied, unless the selected model includes almost all or almost none of the available regressors. For the distribution of confidence interval length, we find that the κ-quantiles behave like 1/(1−κ) for κ close to 1. Our results can also be used to analyze other confidence intervals that are based on the polyhedral method.

Suggested Citation

  • Danijel Kivaranovic & Hannes Leeb, 2021. "On the Length of Post-Model-Selection Confidence Intervals Conditional on Polyhedral Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 845-857, April.
  • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:534:p:845-857
    DOI: 10.1080/01621459.2020.1732989
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    Cited by:

    1. Andrea C. Garcia‐Angulo & Gerda Claeskens, 2023. "Exact uniformly most powerful postselection confidence distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 358-382, March.
    2. Jelle J Goeman & Aldo Solari, 2024. "On selection and conditioning in multiple testing and selective inference," Biometrika, Biometrika Trust, vol. 111(2), pages 393-416.
    3. D García Rasines & G A Young, 2023. "Splitting strategies for post-selection inference," Biometrika, Biometrika Trust, vol. 110(3), pages 597-614.

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