Bootstrap approximation of tail dependence function
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, J. de Ronde, Sea and wind: Multivariate extremes at work, Extremes 1 (1998) 7-45]). A simple, but effective estimator for the tail dependence function is the tail empirical distribution function, see [X. Huang, Statistics of Bivariate Extreme Values, Ph.D. Thesis, Tinbergen Institute Research Series, 1992] or [R. Schmidt, U. Stadtmüller, Nonparametric estimation of tail dependence, Scand. J. Stat. 33 (2006) 307-335]. 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, S.H. Lo, On a mapping approach to investigating the bootstrap accuracy, Probab. Theory Relat. Fields 107 (1997) 197-217], 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.
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Volume (Year): 99 (2008)
Issue (Month): 8 (September)
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References listed on IDEAS
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- Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001.
"Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation,"
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- J. Danielsson & L. de Haan & L. Peng & C.G. de Vries, 1997. "Using a Bootstrap Method to choose the Sample Fraction in Tail Index Estimation," Tinbergen Institute Discussion Papers 97-016/4, Tinbergen Institute.
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- Einmahl, J.H.J. & Ruymgaart, F.H., 1987.
"The almost sure behaviour of the oscillation modulus of the multivariate empirical process,"
Other publications TiSEM
94429b0f-0175-452f-b41b-f, Tilburg University, School of Economics and Management.
- Einmahl, J. H. J. & Ruymgaart, F. H., 1987. "The almost sure behavior of the oscillation modulus of the multivariate empirical process," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 87-96, November.
- Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
- Geluk, J.L. & de Haan, L.F.M., 2002. "On bootstrap sample size in extreme value theory," Econometric Institute Research Papers EI 2002-40, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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