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Rates of convergence in multivariate extreme value theory


  • Omey, E.
  • Rachev, S. T.


We discuss rates of convergence for the distribution of normalized sample extremes to the appropriate limit distribution. We show that the rate of convergence depends on that of the corresponding dependence functions and that of the marginals. The univariate results are well known by now, so we restrict our attention to dependence functions (Sections 2 and 3). In the final section of the paper we obtain a Berry-Esséen type result for multivariate extremes.

Suggested Citation

  • Omey, E. & Rachev, S. T., 1991. "Rates of convergence in multivariate extreme value theory," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 36-50, July.
  • Handle: RePEc:eee:jmvana:v:38:y:1991:i:1:p:36-50

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    References listed on IDEAS

    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    3. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    4. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
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    Cited by:

    1. Omey, Edward & Vesilo, Rein, 2011. "Local limit theorems for shock models," Working Papers 2011/23, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Falk, Michael & Reiss, Rolf Dieter, 2002. "A characterization of the rate of convergence in bivariate extreme value models," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 341-351, October.
    3. de Haan, L. & Peng, L., 1997. "Rates of Convergence for Bivariate Extremes," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 195-230, May.
    4. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.
    5. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
    6. Maejima, Makoto & Rachev, Svetlozar T., 1997. "Rate-of-convergence in the multivariate max-stable limit theorem," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 115-123, March.


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