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# Best Subset Binary Prediction

Listed:
• Le-Yu Chen
• Sokbae Lee

## 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

• Le-Yu Chen & Sokbae Lee, 2016. "Best Subset Binary Prediction," Papers 1610.02738, arXiv.org, revised May 2018.
• Handle: RePEc:arx:papers:1610.02738
as

File URL: http://arxiv.org/pdf/1610.02738

## References listed on IDEAS

as
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## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Jiun-Hua Su, 2019. "Model Selection in Utility-Maximizing Binary Prediction," Papers 1903.00716, arXiv.org.
2. 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.
3. Eric Mbakop & Max Tabord-Meehan, 2016. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Papers 1609.03167, arXiv.org, revised Dec 2019.
4. Le-Yu Chen & Sokbae Lee, 2018. "High Dimensional Classification through $\ell_0$-Penalized Empirical Risk Minimization," Papers 1811.09540, arXiv.org.
5. Max Tabord-Meehan, 2018. "Stratification Trees for Adaptive Randomization in Randomized Controlled Trials," Papers 1806.05127, arXiv.org, revised Jan 2020.
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. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Nov 2019.

### 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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