Copula-based conditional tail indices

Abstract

Consider a multivariate distribution of (X,Y), where X is a vector of predictor variables and Y is a response variable. Results are obtained for comparing the conditional and marginal tail indices, ξY|X(x) and ξY, based on conditional distributions {FY|X(⋅|x)} and marginal distribution FY, respectively. For a multivariate distribution based on a copula, the conditional tail index can be decomposed into a product of copula-based conditional tail indices and the marginal tail index. In some applications, one may want ξY|X(x) to be non-constant, and some new copula families are derived to facilitate this.