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Honest confidence regions for a regression parameter in logistic regression with a large number of controls

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  • Alexandre Belloni
  • Victor Chernozhukov
  • Ying Wei
Abstract
This paper considers inference in logistic regression models with high dimensional data. We propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α0 a parameter in front of the regressor of interest, such as the treatment variable or policy variable. These methods allow to estimate α0 at the root-n rate when the total number p of other regressors, called controls, exceed the sample size n, using the sparsity assumptions. The sparsity assumption means that only s unknown controls are needed to accurately approximate the nuisance part of the regression function, where s is smaller than n. Importantly, the estimators and these resulting confidence regions are 'honest' in the formal sense that their properties hold uniformly over s-sparse models. Moreover, these procedures do not rely on traditional 'consistent model selection' arguments for their validity; in fact, they are robust with respect to 'moderate' model selection mistakes in variable selection steps. Moreover, the estimators are semi-parametrically efficient in the sense of attaining the semi-parametric efficiency bounds for the class of models in this paper.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2013. "Honest confidence regions for a regression parameter in logistic regression with a large number of controls," CeMMAP working papers 67/13, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:67/13
    DOI: 10.1920/wp.cem.2013.6713
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    1. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016057, September.
    2. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    3. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Robust inference in high-dimensional approximately sparse quantile regression models," CeMMAP working papers 70/13, Institute for Fiscal Studies.
    4. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107674165, September.
    5. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    6. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016064, September.
    7. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression models," CeMMAP working papers CWP24/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107627314, September.
    9. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016040, September.
    10. 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.
    11. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107638105, September.
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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2019. "Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 749-758, April.
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Robust inference in high-dimensional approximately sparse quantile regression models," CeMMAP working papers CWP70/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Yichen Gao & Yu Zhang & Ximing Wu, 2015. "Penalized exponential series estimation of copula densities with an application to intergenerational dependence of body mass index," Empirical Economics, Springer, vol. 48(1), pages 61-81, February.
    5. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    6. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    7. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "High-Dimensional Methods and Inference on Structural and Treatment Effects," Journal of Economic Perspectives, American Economic Association, vol. 28(2), pages 29-50, Spring.
    8. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
    9. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    10. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Alexandre Belloni & Victor Chernozhukov & Lie Wang, 2013. "Pivotal estimation via square-root lasso in nonparametric regression," CeMMAP working papers 62/13, Institute for Fiscal Studies.
    12. Stijn Vansteelandt & Oliver Dukes, 2022. "Assumption‐lean inference for generalised linear model parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 657-685, July.
    13. Barbara Felderer & Jannis Kueck & Martin Spindler, 2021. "Big Data meets Causal Survey Research: Understanding Nonresponse in the Recruitment of a Mixed-mode Online Panel," Papers 2102.08994, arXiv.org.
    14. van de Geer, Sara, 2016. "Worst possible sub-directions in high-dimensional models," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 248-260.
    15. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    16. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2013. "Supplementary Appendix for "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls"," Papers 1305.6099, arXiv.org, revised Jun 2013.

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