Parametric models for tail copulas are being used for modeling tail dependence and maximum likelihood estimation is employed to estimate unknown parameters. However, two important questions seem unanswered in the literature: (1) What is the asymptotic distribution of the MLE and (2) how does one test the parametric model? In this paper, we answer these two questions in the case of a single parameter for ease of illustration. A simulation study is provided to investigate the finite sample performance of the proposed estimator and test.

Empirical tail copula, Extreme values, Maximum likelihood estimation, Tail copula,
Journal of Multivariate Analysis
Tinbergen Institute

de Haan, L.F.M, Neves, C, & Peng, L. (2008). Parametric tail copula estimation and model testing. Journal of Multivariate Analysis, 99(6), 1260–1275. doi:10.1016/j.jmva.2007.08.003