摘要翻译：
我们考虑了一个二元结果预测的变量选择问题。我们研究了最优子集选择过程，通过最大化Manski(1975，1985)的最大得分目标函数来选择协变量，并以最大选择变量数为约束。我们证明了这一过程可以等价地转化为求解一个混合整数优化问题，从而可以计算精确解或具有一定逼近误差界的近似解。根据理论结果，当潜在协变量的维数可能远大于样本量时，我们得到了非渐近的风险上界和风险下界。当所选变量的最大个数不变且不随样本量增加时，我们的上下风险界都是极小极大率最优的。通过蒙特卡罗模拟和工作-出行交通方式选择的实证应用，说明了最优子集二元预测方法的有效性。
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英文标题：
《Best Subset Binary Prediction》
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作者：
Le-Yu Chen, Sokbae Lee
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最新提交年份：
2018
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  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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PDF链接：
https://arxiv.org/pdf/1610.02738