Marginal empirical likelihood and sure independence feature screening
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边际经验似然与确定独立特征筛选
- 研究问题
- 当变量数量随样本量呈指数增长时，如何利用边际信息筛选与响应有关的变量，并将估计不确定性纳入筛选？
- 方法与思路
- 作者以参数取零时的边际经验似然比作为筛选依据，构造适用于线性模型、广义线性模型及一般矩条件的程序。
- 材料陈述的贡献
- 摘要称该方法借助经验似然的自学生化性质纳入不确定性，对分布假设限制较少，并提供理论和数值研究支持。
- 阅读关注点
- 应核对筛选阈值、信号强度与变量依赖条件，以及确定筛选保证和一般矩条件扩展分别覆盖哪些情形。
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- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未列出具体假设、误选控制或比较结果，不能据此认定普遍优越。
原文摘要
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.