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Bootstrap approximation of tail dependence function

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  • Peng, Liang
  • Qi, Yongcheng

Abstract

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.

Suggested Citation

  • Peng, Liang & Qi, Yongcheng, 2008. "Bootstrap approximation of tail dependence function," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1807-1824, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1807-1824
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    References listed on IDEAS

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    1. 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," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. 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.
    3. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    4. 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.
    5. 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.
    6. EL-NOUTY Charles & GUILLOU Armelle, 2000. "On The Bootstrap Accuracy Of The Pareto Index," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 275-290, March.
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    Cited by:

    1. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    2. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    3. Bücher Axel, 2014. "A note on nonparametric estimation of bivariate tail dependence," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-12, June.

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