Expected Conditional Characteristic Function-based Measures for Testing Independence

• 成果类型: Article
• 署名作者: Ke, Chenlu; Yin, Xiangrong
• 署名单位: University of Kentucky
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1604364
• 发表日期: 2020
• 页码: 985-996
• 关键词: dimension reduction; distance; dependence

摘要

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. for this article are available online.