Nonparametric Estimation of the Tail-Dependence Coefficient

Abstract

A common measure of tail dependence is the so-called tail-dependence coefficient. We present a nonparametric estimator of the tail-dependence coefficient and prove its strong consistency and asymptotic normality in the case of known marginal distribution functions. The finite-sample behavior as well as robustness will be assessed through simulation. Although it has a good performance, it is sensitive to the extreme value dependence assumption. We shall see that a block maxima procedure might improve the estimation. This will be illustrated through simulation. An application to financial data shall be presented at the end.

Keywords

• extreme value theory
• stable tail dependence function
• tail-dependence coefficient