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Projection correlation between scalar and vector variables and its use in feature screening with multi-response data

机译:标量和矢量变量与多响应数据的特征筛选的预测相关性

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In this article, we introduce a new methodology to perform feature screening for ultrahigh dimensional data with multivariate responses. Several extant screening procedures are available for multivariate responses, but they may be adversely affected by heavy-tailed observations or the dimension of multivariate responses. In order to attack these challenges, we first introduce a nonparametric coefficient, called projection correlation, to measure the departure of dependence between a scalar variable X and a vector variable . It takes values between zero and one, does not require any moment conditions on X and , and is zero if and only if X and are independent. Based on its estimation that has desirable theoretical properties, such as algebraic simplicity and consistency, we present a novel sure independence screening procedure, which enjoys the desirable sure screening property. Numerical results demonstrate the effectiveness of the proposed procedure in comparison with the existing counterparts.
机译:在本文中,我们介绍了一种新的方法,可以使用多元响应来执行用于超高尺寸数据的特征筛选。几个现存的筛选程序可用于多变量反应,但它们可能因重尾观察或多变量反应的尺寸而受到不利影响。为了攻击这些挑战,我们首先引入非参数系数,称为投影相关性,以测量标量x和矢量变量之间依赖的偏离。它在零和一个之间取得值,不需要X上的任何时刻条件,并且才能零,如果X并且是独立的。基于其具有所需理论性质的估计,例如代数简单性和一致性,我们提出了一种新颖的独立筛选程序,它可以享有所需的筛选性。数值结果证明了与现有对应物相比的提出程序的有效性。

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