Best subset binary prediction
Le-Yu Chen () and
Sokbae (Simon) Lee ()
No CWP50/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the explanatory variables are chosen by maximizing Manski (1975, 1985)'s maximum score type 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 (MIO) problem, which enables computation of the exact or an approximate solution with a de finite 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 fi xed 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.
Keywords: binary choice; maximum score estimation; best subset selection; `0-constrained maximization; mixed integer optimization; minimax optimality; fi nite sample property (search for similar items in EconPapers)
JEL-codes: C52 C53 C55 (search for similar items in EconPapers)
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Journal Article: Best subset binary prediction (2018)
Working Paper: Best Subset Binary Prediction (2018)
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