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Bootstrap approximation of tail dependence function. (English) Zbl 1284.62301

Summary: For estimating a rare event via the multivariate extreme value theory, the so-called tail dependence function has to be investigated (see [L. de Haan and J. de Ronde, Extremes 1, No. 1, 7–46 (1998; Zbl 0921.62144)]). A simple, but effective estimator for the tail dependence function is the tail empirical distribution function, see [X. Huang, “Statistics of bivariate extreme values”, Tinbergen Institute Research Series, Ph.D. Thesis (1992); R. Schmidt and U. Stadtmüller, Scand. J. Stat. 33, No. 2, 307–335 (2006; Zbl 1124.62016)]. In this paper, we first derive a bootstrap approximation for a tail dependence function with an approximation rate via the construction approach developed by K. Chen and S.-H. Lo [Probab. Theory Relat. Fields 107, No. 2, 197–217 (1997; Zbl 0868.60033)], and then apply it to construct a confidence band for the tail dependence function. A simulation study is conducted to assess the accuracy of the bootstrap approach.

MSC:

62G32 Statistics of extreme values; tail inference
62G09 Nonparametric statistical resampling methods
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