Bootstrap approximation of tail dependence function

Authors:
Liang Peng;Yongcheng Qi
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;Department of Mathematics and Statistics, University of Minnesota Duluth, SCC 140, 1117 University Drive, Duluth, MN 55812, USA
Venue:
Journal of Multivariate Analysis
Year:
2008

Citing 3
Cited 0

Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems

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Best attainable rates of convergence for estimators of the stable tail dependence function

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Using a bootstrap method to choose the sample fraction in tail index estimation

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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. Stadtmuller, 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.