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Testing-Based Forward Model Selection

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  • Damian Kozbur

Abstract

This paper introduces and analyzes a procedure called Testing-Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for deciding which covariate to include next and when to stop including covariates is derived from a profile of traditional statistical hypothesis tests. This paper proves probabilistic bounds for prediction error and the number of selected covariates, which depend on the quality of the tests. The bounds are then specialized to a case with heteroskedastic data with tests derived from Huber-Eicker-White standard errors. TBFMS performance is compared to Lasso and Post-Lasso in simulation studies. TBFMS is then analyzed as a component into larger post-model selection estimation problems for structural economic parameters. Finally, TBFMS is used to illustrate an empirical application to estimating determinants of economic growth.

Suggested Citation

  • Damian Kozbur, 2015. "Testing-Based Forward Model Selection," ECON - Working Papers 283, Department of Economics - University of Zurich, revised Apr 2018.
    • Handle: RePEc:zur:econwp:283
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    References listed on IDEAS

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    1. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2016. "Inference in High-Dimensional Panel Models With an Application to Gun Control," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 590-605, October.
    2. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    3. 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.
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    18. Damian Kozbur, 2017. "Sharp convergence rates for forward regression in high-dimensional sparse linear models," ECON - Working Papers 253, Department of Economics - University of Zurich, revised Apr 2018.
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    Cited by:

    1. 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.
    2. Sarra Houidi & Dominique Fourer & François Auger & Houda Ben Attia Sethom & Laurence Miègeville, 2021. "Comparative Evaluation of Non-Intrusive Load Monitoring Methods Using Relevant Features and Transfer Learning," Energies, MDPI, vol. 14(9), pages 1-28, May.
    3. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    4. 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.
    5. 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 Dec 2017.
    6. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    7. Peter C.B. Phillips & Zhentao Shi, 2019. "Boosting the Hodrick-Prescott Filter," Cowles Foundation Discussion Papers 2192, Cowles Foundation for Research in Economics, Yale University.
    8. Jooyoung Cha & Harold D. Chiang & Yuya Sasaki, 2021. "Inference in high-dimensional regression models without the exact or $L^p$ sparsity," Papers 2108.09520, arXiv.org, revised Dec 2022.
    9. Damian Kozbur, 2017. "Sharp convergence rates for forward regression in high-dimensional sparse linear models," ECON - Working Papers 253, Department of Economics - University of Zurich, revised Apr 2018.
    10. Zhentao Shi & Jingyi Huang, 2019. "Forward-Selected Panel Data Approach for Program Evaluation," Papers 1908.05894, arXiv.org, revised Apr 2021.
    11. Shi, Zhentao & Huang, Jingyi, 2023. "Forward-selected panel data approach for program evaluation," Journal of Econometrics, Elsevier, vol. 234(2), pages 512-535.

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    More about this item

    Keywords

    Model selection; forward regression; sparsity; hypothesis testing;
    All these keywords.

    JEL classification:

    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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