Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening
Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening
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DOI：
10.1080/01621459.2014.887012
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发表时间：
2014-07-03
影响因子：
3.7
通讯作者：
Zhang, Jingsi
中科院分区：
文献类型：
--
作者：
Shao, Xiaofeng;Zhang, Jingsi
在这篇文章中，我们提出了一个新的度量，所谓的鞅差相关性，来衡量一个标量响应变量V和一个向量预测变量U之间的条件均值独立性的偏离。我们的度量是Szekely，Rizzo和Bahirov提出的距离相关性的自然扩展，用于测量V和U之间的依赖性。鞅差相关和它的经验对应物继承了距离相关和样本距离相关的一些理想的特征，例如代数简单性和优雅的理论性质。我们进一步使用鞅差相关作为边际效用来进行高维变量筛选，以筛选出对给定协变量的响应的条件均值没有贡献的变量。条件分位数筛选的进一步扩展也进行了详细描述，并严格证明了筛选属性。仿真结果和真实的数据实例表明，与现有的同行相比，基于鞅差相关的筛选程序的有效性。本文的补充材料可在网上查阅。
In this article, we propose a new metric, the so-called martingale difference correlation, to measure the departure of conditional mean independence between a scalar response variable V and a vector predictor variable U. Our metric is a natural extension of distance correlation proposed by Szekely, Rizzo, and Bahirov, which is used to measure the dependence between V and U. The martingale difference correlation and its empirical counterpart inherit a number of desirable features of distance correlation and sample distance correlation, such as algebraic simplicity and elegant theoretical properties. We further use martingale difference correlation as a marginal utility to do high-dimensional variable screening to screen out variables that do not contribute to conditional mean of the response given the covariates. Further extension to conditional quantile screening is also described in detail and sure screening properties are rigorously justified. Both simulation results and real data illustrations demonstrate the effectiveness of martingale difference correlation-based screening procedures in comparison with the existing counterparts. Supplementary materials for this article are available online.