A new look at measuring dependence

This paper revisits the concept of dependence. We view statistical dependence as the state of variables being influenced by others. Our viewpoint accords well with the daily understanding of the notion of dependence, while classical dependence measures such as Pearson’s correlation coefficient, Kendall’s τ and Spearman’s ρ have different meanings. With this understanding of dependence, we introduce new dependence measures which are easy to work with and they are useful for developing an asymptotic theory for complicated stochastic systems. We also explore relations of the introduced dependence concept with nonlinear system theory, experimental design, information theory and risk management.