Complete dependence everywhere?

Abstract

Describing the situation of full predictability of a random variable Y given the value of another random variable X, the notion of complete dependence might seem far too restrictive to be of any practical importance at first glance. Recent results have shown, however, that complete dependence naturally appears in various settings. This chapter will therefore sketch some problems related to complete dependence. Doing so, the focus will be on dependence measures strictly separating extreme dependence concepts, on a problem related to joint-default maximization, on a question from uniform distribution theory, and on the relationship between the two most well-known measures of concordance, Kendall’s τ and Spearman’s ρ. A short excursion to topology showing that complete dependence is not atypical at all complements the chapter.