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Best subset binary prediction

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  • Chen, Le-Yu
  • Lee, Sokbae

Abstract

We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)’s maximum score objective function subject to a constraint on the maximal number of selected variables. We show that this procedure can be equivalently reformulated as solving a mixed integer optimization problem, which enables computation of the exact or an approximate solution with a definite approximation error bound. In terms of theoretical results, we obtain non-asymptotic upper and lower risk bounds when the dimension of potential covariates is possibly much larger than the sample size. Our upper and lower risk bounds are minimax rate-optimal when the maximal number of selected variables is fixed and does not increase with the sample size. We illustrate usefulness of the best subset binary prediction approach via Monte Carlo simulations and an empirical application of the work-trip transportation mode choice.

Suggested Citation

  • Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
  • Handle: RePEc:eee:econom:v:206:y:2018:i:1:p:39-56
    DOI: 10.1016/j.jeconom.2018.05.001
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    Citations

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    Cited by:

    1. Le‐Yu Chen & Sokbae Lee, 2018. "Exact computation of GMM estimators for instrumental variable quantile regression models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 553-567, June.
    2. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Nov 2019.
    3. Max Tabord-Meehan, 2018. "Stratification Trees for Adaptive Randomization in Randomized Controlled Trials," Papers 1806.05127, arXiv.org, revised Jan 2020.
    4. Eric Mbakop & Max Tabord-Meehan, 2016. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Papers 1609.03167, arXiv.org, revised Dec 2019.
    5. Jiun-Hua Su, 2019. "Model Selection in Utility-Maximizing Binary Prediction," Papers 1903.00716, arXiv.org.
    6. Bilias, Yannis & Florios, Kostas & Skouras, Spyros, 2019. "Exact computation of Censored Least Absolute Deviations estimator," Journal of Econometrics, Elsevier, vol. 212(2), pages 584-606.
    7. Le-Yu Chen & Sokbae Lee, 2018. "High Dimensional Classification through $\ell_0$-Penalized Empirical Risk Minimization," Papers 1811.09540, arXiv.org.

    More about this item

    Keywords

    Binary choice; Maximum score estimation; Best subset selection; ℓ0-constrained maximization; Mixed integer optimization; Minimax optimality; Finite sample property;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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