MARGINAL EMPIRICAL LIKELIHOOD AND SURE INDEPENDENCE FEATURE SCREENING.
MARGINAL EMPIRICAL LIKELIHOOD AND SURE INDEPENDENCE FEATURE SCREENING.
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DOI：
10.1214/13-aos1139
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发表时间：
2013-08-01
影响因子：
4.5
通讯作者：
Wu Y
中科院分区：
文献类型：
--
作者：
Chang J;Tang CY;Wu Y
我们研究了边际经验似然方法的情况下，当变量的数量呈指数增长的样本量。边际经验似然比作为感兴趣的参数的函数进行了系统的研究，我们发现，边际经验似然比评估为零，可以用来区分解释变量是否有助于响应变量或没有。基于这一发现，我们提出了一个统一的线性模型和广义线性模型的特征筛选过程。不同于大多数现有的特征筛选方法，依赖于一些边际估计的幅度来识别真实信号，所提出的筛选方法是能够进一步纳入这样的估计的不确定性的水平。这样的优点继承了经验似然方法的自学生化属性，并扩展了现有特征筛选方法的见解。此外，我们表明，我们的筛选方法是限制较少的分布假设，并可以方便地适用于广泛的场景，如使用一般矩条件指定的模型。我们的理论结果和大量的数值模拟和数据分析的例子证明了边际经验似然方法的优点。
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.