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Exact post-selection inference for adjusted R squared selection

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  • Pirenne, Sarah
  • Claeskens, Gerda

Abstract

Post-selection inference is developed for regression coefficients selected by the widely used model selection technique of adjusted R2. Selective inference deals with the selection aspect by conditioning inference on the model selection event. In linear models, we obtain exact post-selection inference in finite samples. Extensions to logistic regression models are discussed. A simulation study illustrates the exact type I error control, unlike classical inference. Our tests provide higher power than data splitting approaches.

Suggested Citation

  • Pirenne, Sarah & Claeskens, Gerda, 2024. "Exact post-selection inference for adjusted R squared selection," Statistics & Probability Letters, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:stapro:v:211:y:2024:i:c:s0167715224001020
    DOI: 10.1016/j.spl.2024.110133
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    References listed on IDEAS

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    1. Rügamer, David & Greven, Sonja, 2018. "Selective inference after likelihood- or test-based model selection in linear models," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 7-12.
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    4. 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.
    5. Ali Charkhi & Gerda Claeskens, 2018. "Asymptotic post-selection inference for the Akaike information criterion," Biometrika, Biometrika Trust, vol. 105(3), pages 645-664.
    6. Ryan J. Tibshirani & Jonathan Taylor & Richard Lockhart & Robert Tibshirani, 2016. "Exact Post-Selection Inference for Sequential Regression Procedures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 600-620, April.
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