Asymmetric Dependence Measurement and Testing

TL;DR

This paper discusses the limitations of symmetric dependence measures, advocates for asymmetric measures like Vinod's R*, and introduces statistical inference methods to test dependence direction with greater power.

Contribution

It introduces statistical inference techniques for Vinod's asymmetric dependence measure R*, enhancing the ability to test dependence direction.

Findings

Asymmetry in dependence measures is common in real-world data.

Proposed tests have higher power when the dependence direction is known.

Bootstrap methods improve inference accuracy for R*.

Abstract

Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the sense that the strength of dependence of Xi on Xj exactly equals the strength of dependence of Xj on Xi. However, we show that such symmetry is often untrue in many real-world examples, being neither necessary nor sufficient. Vinod's (2014) asymmetric matrix R* in [-1, 1] of generalized correlation coefficients provides intuitively appealing, readily interpretable, and superior measures of dependence. This paper proposes statistical inference for R* using Taraldsen's (2021) exact sampling distribution of correlation coefficients and the bootstrap. When the direction is known, proposed asymmetric (one-tail) tests have greater power.