arXiv 9 Oct 2016 · Statistics — Methodology · publishedJournal of Econometrics (2018) · 20 citations (OpenAlex)
arXiv:1610.02738 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Jiang and Tanner (2010) Risk Minimization for Time Series Binary Choice with Variable Selection | 1.000 | 7 | 4 | 100% |
| 2 | Florios and Skouras (2008) Exact computation of max weighted score estimators | 0.953 | 15 | 4 | 87% |
| 3 | Raskutti, Wainwright, and Yu (2011) Minimax rates of estimation for high-dimensional linear regression over lq-balls | 0.941 | 6 | 3 | 83% |
| 4 | Manski (1975) Maximum score estimation of the stochastic utility model of choice | 0.928 | 4 | 4 | 100% |
| 5 | Manski (1985) Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator | 0.928 | 4 | 4 | 100% |
| 6 | Greenshtein (2006) Best subset selection, persistence in high-dimensional statistical learning and optimization under $L_1$ constraint | 0.874 | 7 | 2 | 100% |
| 7 | Kitagawa and Tetenov (2018) Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice | 0.874 | 6 | 2 | 100% |
| 8 | Bertsimas, King, and Mazumder (2016) Best subset selection via a modern optimization lens | 0.874 | 6 | 2 | 100% |
| 9 | Horowitz (1993) Semiparametric estimation of a work-trip mode choice model | 0.874 | 5 | 2 | 100% |
| 10 | Tsybakov (2004) Optimal aggregation of classifiers in statistical learning | 0.874 | 5 | 2 | 100% |
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