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Best subset binary prediction
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DOI：10.1016/j.jeconom.2018.05.001.png)
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Abstract
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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. (C) 2018 The Author(s). Published by Elsevier B.V.
Keywords:
Binary choice
Maximum score estimation
Best subset selection
l(0)-constrained maximization
Mixed integer optimization
Minimax optimality
Finite sample property
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