Measures of Dependence for Nonlinear Association and the Hypothetical Tests

• Activity Number: 297
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Jungwon Mun*+ and Jee Young Moon
• Companies: and University of Wisconsin-Madison
• Keywords: Correlation ; Dependence ; Pearson ; Conditional Expectation

Abstract

As high dimensional data arise often in modern studies, correlation measures have recently regained the attention of researchers in many fields such as genetics. Dimension reduction becomes a major concern in high dimensional data and correlation measures play a key role in it. There are various correlation measures, but many of them easily fail to detect nonlinear relationship, and are restricted to numerical variables. In 2005, Hsing et al introduced a new measure, called Coefficient of intrinsic dependence (CID) that overcomes drawbacks and broadens the applicable area. CID compares the conditional information of Y on X with the marginal information of Y. The authors proposed a computational approach to calculate CID(Y|X) and demonstrate the advantages of the measure. As we have studied and investigated the CID, we found a way to refine the measure that improves its performances and a more logical way to compare the behaviors of CID with other correlation measures. In addition to these, we derived theoretical relationships between CID and ANOVA. Various simulations and figures are presented illustrating the updated behaviors of CID and our claims of its relevance with ANOVA.