Copula-based conditional tail indices

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, eY|X(x) and eY, based on conditional distributions {FY|X(& sdot;|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 eY|X(x) to be non -constant, and some new copula families are derived to facilitate this.