IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v211y2024ics0167715224001020.html
   My bibliography  Save this article

Exact post-selection inference for adjusted R squared selection

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224001020
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110133?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Ali Charkhi & Gerda Claeskens, 2018. "Asymptotic post-selection inference for the Akaike information criterion," Biometrika, Biometrika Trust, vol. 105(3), pages 645-664.
    3. Snigdha Panigrahi & Jonathan Taylor, 2023. "Approximate Selective Inference via Maximum Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2810-2820, October.
    4. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. 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.
    4. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
    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. Tindara Addabbo & Anna Maccagnan & Carmen Llorca-Rodríguez & Rosa García-Fernández, 2010. "Income distribution and the effect of the financial crisis on the Italian and Spanish labour markets," Department of Economics 0639, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    7. Walter Beckert, 2015. "Choice in the Presence of Experts," Birkbeck Working Papers in Economics and Finance 1503, Birkbeck, Department of Economics, Mathematics & Statistics.
    8. Clarke, Judith A., 2008. "On weighted estimation in linear regression in the presence of parameter uncertainty," Economics Letters, Elsevier, vol. 100(1), pages 1-3, July.
    9. Zhenlin Yang, 2006. "On Joint Modelling and Testing for Local and Global Spatial Externalities," Development Economics Working Papers 22487, East Asian Bureau of Economic Research.
    10. Dufour, J.M., 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    12. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    13. Okhrin, Ostap & Ristig, Alexander & Sheen, Jeffrey R. & Trück, Stefan, 2015. "Conditional systemic risk with penalized copula," SFB 649 Discussion Papers 2015-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Xiaohong Chen & Roger Koenker & Zhijie Xiao, 2009. "Copula-based nonlinear quantile autoregression," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 50-67, January.
    15. Jan R. Magnus & Wendun Wang & Xinyu Zhang, 2016. "Weighted-Average Least Squares Prediction," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1040-1074, June.
    16. Giacomini, Raffaella & Ragusa, Giuseppe, 2011. "Incorporating theoretical restrictions into forecasting by projection methods," CEPR Discussion Papers 8604, C.E.P.R. Discussion Papers.
    17. Magnus, Jan R., 2007. "The Asymptotic Variance Of The Pseudo Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 23(5), pages 1022-1032, October.
    18. Drew Creal & Siem Jan Koopman & André Lucas & Marcin Zamojski, 2015. "Generalized Autoregressive Method of Moments," Tinbergen Institute Discussion Papers 15-138/III, Tinbergen Institute, revised 06 Jul 2018.
    19. Magnus, Jan & Peresetsky, Anatoly, 2010. "The price of Moscow apartments," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 17(1), pages 89-105.
    20. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:211:y:2024:i:c:s0167715224001020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.