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A note on nonparametric estimation of bivariate tail dependence. (English) Zbl 1418.62216

Summary: Nonparametric estimation of tail dependence can be based on a standardization of the marginals if their cumulative distribution functions are known. In this paper it is shown to be asymptotically more efficient if the additional knowledge of the marginals is ignored and estimators are based on ranks. The discrepancy between the two estimators is shown to be substantial for the popular Clayton and Gumbel-Hougaard models. A brief simulation study indicates that the asymptotic conclusions transfer to finite samples.

MSC:

62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

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