论文标题
通过经验可能性进行多响应线性模型的功能筛选
Feature screening for multi-response linear models by empirical likelihood
论文作者
论文摘要
本文提出了一种通过经验可能性的多响应超高维线性模型的新功能筛选方法。通过多元瞬间条件，经验可能性诱导的排名统计数据可以利用响应之间的关节效应，因此比单独考虑响应的方法的性能要好得多。更重要的是，通过使用经验可能性，新方法适应了随机误差的条件差异中的异质性。新提出的方法的肯定筛选属性通过在合理的规模内控制的模型大小证明。此外，新的筛选方法还扩展到有条件的版本，因此它可以恢复隐藏的预测变量，而隐藏的预测变量很容易被无条件的方法遗漏。还提供了相应的理论属性。最后，提供了数值研究和实际数据分析，以说明所提出方法的有效性。
This paper proposes a new feature screening method for the multi-response ultrahigh dimensional linear model by empirical likelihood. Through a multivariate moment condition, the empirical likelihood induced ranking statistics can exploit the joint effect among responses, and thus result in a much better performance than the methods considering responses individually. More importantly, by the use of empirical likelihood, the new method adapts to the heterogeneity in the conditional variance of random error. The sure screening property of the newly proposed method is proved with the model size controlled within a reasonable scale. Additionally, the new screening method is also extended to a conditional version so that it can recover the hidden predictors which are easily missed by the unconditional method. The corresponding theoretical properties are also provided. Finally, both numerical studies and real data analysis are provided to illustrate the effectiveness of the proposed methods.
