MEASURING AND TESTING FOR INTERVAL QUANTILE DEPENDENCE

• 成果类型: Article
• 署名作者: Zhu, Liping; Zhang, Yaowu; Xu, Kai
• 署名单位: Renmin University of China; Shanghai University of Finance & Economics; Shanghai University of Finance & Economics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1635
• 发表日期: 2018
• 页码: 2683-2710
• 关键词: martingale difference correlation; dimensional heterogeneous data; linear-models; covariance; regression; parameter; distances; SPACE

摘要

In this article, we introduce the notion of interval quantile independence which generalizes the notions of statistical independence and quantile independence. We suggest an index to measure and test departure from interval quantile independence. The proposed index is invariant to monotone transformations, nonnegative and equals zero if and only if the interval quantile independence holds true. We suggest a moment estimate to implement the test. The resultant estimator is root-n-consistent if the index is positive and n-consistent otherwise, leading to a consistent test of interval quantile independence. The asymptotic distribution of the moment estimator is free of parent distribution, which facilitates to decide the critical values for tests of interval quantile independence. When our proposed index is used to perform feature screening for ultrahigh dimensional data, it has the desirable sure screening property.