Dependence Testing via Extremes for Regularly Varying Models

In heavy-tailed data, such as data drawn from regularly varying models, extreme values can occur relatively often. As a consequence, in the context of hypothesis testing, extreme values can provide valuable information in identifying dependence between two data sets. In this paper, the error exponent of a dependence test is studied when only processed data recording whether or not the value of the data exceeds a given value is available. An asymptotic approximation of the error exponent is obtained, establishing a link with the upper tail dependence, which is a key quantity in extreme value theory. While the upper tail dependence has been well characterized for elliptically distributed models, much less is known in the non-elliptical setting. To this end, a family of non-elliptical distributions with regularly varying tails arising from shot noise is studied, and an analytical expression for the upper tail dependence derived.