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Exact uniformly most powerful postselection confidence distributions

Author

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  • Andrea C. Garcia‐Angulo
  • Gerda Claeskens

Abstract

A conditioning on the event of having selected one model from a set of possibly misspecified normal linear regression models leads to the construction of uniformly optimal conditional confidence distributions. They can be used for valid postselection inference. The constructed conditional confidence distributions are finite sample exact and encompass all information regarding the focus parameter in the selected model. This includes the construction of optimal postselection confidence intervals at all significance levels and uniformly most powerful hypothesis tests.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:1:p:358-382
    DOI: 10.1111/sjos.12581
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    References listed on IDEAS

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    1. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    2. 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.
    3. Xiaoying Tian & Joshua R Loftus & Jonathan E Taylor, 2018. "Selective inference with unknown variance via the square-root lasso," Biometrika, Biometrika Trust, vol. 105(4), pages 755-768.
    4. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    5. Tore Schweder & Nils Lid Hjort, 2002. "Confidence and Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(2), pages 309-332, June.
    6. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, Enero-Abr.
    7. Xiaoying Tian & Jonathan Taylor, 2017. "Asymptotics of Selective Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 480-499, June.
    8. 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.
    9. Bo Henry Lindqvist & Gunnar Taraldsen, 2005. "Monte Carlo conditioning on a sufficient statistic," Biometrika, Biometrika Trust, vol. 92(2), pages 451-464, June.
    10. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    11. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, Enero-Abr.
    12. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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    Cited by:

    1. Andrea C. Garcia-Angulo & Gerda Claeskens, 2025. "Bootstrap for inference after model selection and model averaging for likelihood models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(3), pages 311-340, April.
    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. Pirenne, Sarah & Claeskens, Gerda, 2024. "Exact post-selection inference for adjusted R squared selection," Statistics & Probability Letters, Elsevier, vol. 211(C).

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