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Post-Selection Inference for Generalized Linear Models with Many Controls

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  • Alexandre Belloni
  • Victor Chernozhukov
  • Ying Wei

Abstract

This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes and apply it to the case of logistic binary choice model. More specifically we propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest $\alpha_0$, a parameter in front of the regressor of interest, such as the treatment variable or a policy variable. These methods allow to estimate $\alpha_0$ at the root-$n$ rate when the total number $p$ of other regressors, called controls, potentially exceed the sample size $n$ using sparsity assumptions. The sparsity assumption means that there is a subset of $s

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  • Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2013. "Post-Selection Inference for Generalized Linear Models with Many Controls," Papers 1304.3969, arXiv.org, revised Mar 2016.
  • Handle: RePEc:arx:papers:1304.3969
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    1. 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.
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    3. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," Review of Economic Studies, Oxford University Press, vol. 81(2), pages 608-650.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    5. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    6. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    7. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    8. Wang, Lie, 2013. "The L1 penalized LAD estimator for high dimensional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 135-151.
    9. 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.
    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.
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    4. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
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    7. Liqian Cai & Arnab Bhattacharjee & Roger Calantone & Taps Maiti, 2019. "Variable Selection with Spatially Autoregressive Errors: A Generalized Moments LASSO Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 146-200, September.
    8. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    9. Alex Coad & Stjepan Srhoj, 2020. "Catching Gazelles with a Lasso: Big data techniques for the prediction of high-growth firms," Small Business Economics, Springer, vol. 55(3), pages 541-565, October.
    10. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    11. Victor Chernozhukov & Vira Semenova, 2018. "Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions," CeMMAP working papers CWP40/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Fang, Tong & Lee, Tae-Hwy & Su, Zhi, 2020. "Predicting the long-term stock market volatility: A GARCH-MIDAS model with variable selection," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 36-49.
    13. Macchiavello, Rocco & Menzel, Andreas & Rabbani, Atonu & Woodruff, Christopher, 2020. "Challenges of Change: An Experiment Promoting Women to Managerial Roles in the Bangladeshi Garment Sector," CEPR Discussion Papers 15085, C.E.P.R. Discussion Papers.
    14. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference in Case-Control Studies," Papers 2004.08318, arXiv.org, revised Oct 2020.
    15. Vira Semenova, 2020. "Better Lee Bounds," Papers 2008.12720, arXiv.org.
    16. Ethan X. Fang & Yang Ning & Han Liu, 2017. "Testing and confidence intervals for high dimensional proportional hazards models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1415-1437, November.
    17. Falco J. Bargagli-Dtoffi & Massimo Riccaboni & Armando Rungi, 2020. "Machine Learning for Zombie Hunting. Firms Failures and Financial Constraints," Working Papers 01/2020, IMT Institute for Advanced Studies Lucca, revised Jun 2020.

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