© 1996 by Biometrika Trust
Statistics for near independence in multivariate extreme values
Department of Mathematical and Computing Sciences, University of Surrey Guildford, Surrey, GU2 5XH, U.K.
Department of Mathematics and Statistics, Lancaster University Lancaster, LA1 4YF, U.K.
We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from this model, we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases. A new parameter which governs the form of dependence is of fundamental importance to this characterisation. By estimating this parameter, we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models. The methods are demonstrated through simulation and by analysing two previously published data sets.
Key Words: Asymptotic independence • Coefficient of tail dependence • Extreme value theory • Generalised Pareto distribution • Maximum likelihood • Multivariate extreme value distribution • Nonregular estimation • Poisson process • Threshold exceedance
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  S.-H. Poon, M. Rockinger, and J. Tawn Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications Rev. Financ. Stud., April 1, 2004; 17(2): 581 - 610. [Abstract] [Full Text] [PDF]
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