Copula-Based Dependence Measures For Piecewise Monotonicity

Abstract

The aim of the present paper is to develop and examine association coefficients which can be helpfully applied in the framework of regression analysis. The construction of the coeffiecients is connected with the well-known Spearman coeffiecient and extensions of it (see Liebscher [5]). The proposed coeffiecient measures the discrepancy between the data points and a function which is strictly increasing on one interval and strictly decreasing in the remaining domain.We prove statements about the asymptotic behaviour of the estimated coeffiecient (convergence rate, asymptotic normality).

Keywords

• dependence measures
• spearman’s 𝜌
• spearman’s footrule
• estimators for dependence measures
• piecewise monotonicity
• 62h20