ABSTRACT
Abstract The dependence among extreme observations is critical in decision making that involves multivariate extreme value analysis. Marginal generalized extreme value distributions coupled with a copula have been applied in practice, but the extreme dependence structure in such models may be limited if the copula is not an extreme value copula. Multivariate extreme value distributions are characterized jointly by marginal generalized extreme value distributions and an extreme-value copula. This chapter reviews multivariate extreme value distributions, extreme value copulas, measures of extremal dependence, multivariate generalized Pareto distributions, semiparemetric conditional dependence models, and their statistical inferences. The multivariate generalized Pareto distribution characterizes the multivariate exceedances over certain thresholds conditioning on that there is at least one marginal exceedance. In the conditional approach, each variable is taken in turn as a conditional variate, given a large value of which, the remaining variables are modeled by their limiting distribution. Parameter estimation and goodness-of-fit test are outlined with references to relevant chapters.
