A new measure of monotone dependence by using Sobolev norms for copula

Abstract

Dependence structure, e.g. measures of dependence, is one of the main studies in correlation analysis. In [10], B. Schweizer and E.F. Wolff used Lp-metric dLp (C, P) to obtain a measure of monotone dependence where P is the product copula or independent copula, and in [11] P. A. Stoimenov defined Sobolev metric ω(C, P) to construct the measure ?(C) for a class of Mutual Complete Dependences (MCDs). Due to the fact that the class of monotone dependence is contained in the class of MCDs, we constructed a new measure of monotone dependence, λ(C), based on Sobolev metric which can be used to characterize comonotonic, countermonotonic and independence.