Detecting a conditional extrme value model

TL;DR

This paper introduces three statistical tools for detecting the conditional extreme value model in bivariate data and distinguishing between different limit measure forms, advancing the analysis of multivariate extreme events.

Contribution

It proposes novel statistics for identifying the conditional extreme value model and differentiating limit measure types in a bivariate setting.

Findings

Three new statistics effectively detect the model

Tools distinguish between two limit measure forms

Enhances multivariate extreme value analysis

Abstract

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in \cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}. In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.