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Estimating a bivariate tail: A copula based approach

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  • Di Bernardino, Elena
  • Maume-Deschamps, Véronique
  • Prieur, Clémentine

Abstract

This paper deals with the problem of estimating the tail of a bivariate distribution function. To this end we develop a general extension of the POT (peaks-over-threshold) method, mainly based on a two-dimensional version of the Pickands–Balkema–de Haan Theorem. We introduce a new parameter that describes the nature of the tail dependence, and we provide a way to estimate it. We construct a two-dimensional tail estimator and study its asymptotic properties. We also present real data examples which illustrate our theoretical results.

Suggested Citation

  • Di Bernardino, Elena & Maume-Deschamps, Véronique & Prieur, Clémentine, 2013. "Estimating a bivariate tail: A copula based approach," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 81-100.
    • Handle: RePEc:eee:jmvana:v:119:y:2013:i:c:p:81-100
    DOI: 10.1016/j.jmva.2013.03.020
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