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Estimating the spectral measure of an extreme value distribution

  • Einmahl, John H.J.
  • de Haan, Laurens
  • Sinha, Ashoke Kumar

Let (X1, Y1), (X2, Y2),..., (Xn, Yn) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.

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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 70 (1997)
Issue (Month): 2 (October)
Pages: 143-171

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Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:143-171
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  1. Deheuvels, Paul & Tiago de Oliveira, José, 1989. "On the non-parametric estimation of the bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 315-323, September.
  2. Deheuvels, Paul, 1991. "On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 429-439, November.
  3. repec:ner:tilbur:urn:nbn:nl:ui:12-125732 is not listed on IDEAS
  4. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
  5. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
  6. Einmahl, J.H.J. & de Haan, L. & Xin, H., 1993. "Estimating a multidimensional extreme-value distribution," Other publications TiSEM 2816eb0c-8f15-4111-94f5-6, Tilburg University, School of Economics and Management.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-125712 is not listed on IDEAS
  8. repec:ner:tilbur:urn:nbn:nl:ui:12-142070 is not listed on IDEAS
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