Exploring the Relationship Between Correlation Coefficients and Dependence Measures in Multivariate Analysis

Posted: Dec 17, 2016

• James Rivera
• Mateo Perez
• Mateo Rivera

Abstract

This research addresses a critical gap in the statistical literature by systematically examining the relationship between traditional correlation coefficients and alternative dependence measures in multivariate settings. While numerous studies have highlighted the shortcomings of Pearson's correlation, few have provided a comprehensive framework for understanding how different dependence measures relate to each other and what aspects of dependence they capture. Our work builds upon the foundational understanding that correlation measures linear relationships, while dependence encompasses a broader spectrum of associations including nonlinear, monotonic, and complex interactive patterns. We propose a novel conceptual framework that distinguishes between different types of dependence and provides guidance on when to use specific dependence measures. This framework acknowledges that no single measure can adequately capture all aspects of multivariate dependence, and that the choice of dependence measure should be informed by the specific characteristics of the data and the research questions being addressed. Our approach integrates insights from information theory, distance-based statistics, and copula theory to develop a more nuanced understanding of multivariate dependence.