A New Epsilon-Local Dependence Measure and Dependence Maps

Abstract

In the present work, we introduce a new local dependence function characterizing dependence structure between two random variables in an $varepsilon$-neighborhood of a particular point from the domain of underlying bivariate distribution and investigate its properties. As an example the local dependence function for Farlie-Gumbel-Morgenstern distribution is provided. Also, we construct dependence maps for some pairs of random variables. We use the estimator of local dependence function to construct the dependence map. Permutation test algorithm is applied for P=500 to obtain more accurate result in dependence map and also several examples are provided.