Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/189780 
Year of Publication: 
2017
Series/Report no.: 
cemmap working paper No. CWP50/17
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
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 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.
Subjects: 
binary choice
maximum score estimation
best subset selection
l 0-constrained maximization
mixed integer optimization
minimaxoptimality
nite sample property
JEL: 
C52
C53
C55
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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