Abstract
Suppose that the underlying distribution function is ultimately continuous and strictly increasing. In this case the rate of joint convergence of the k largest order statistics, equally standardized, in a sample of n i.i.d. random variables is O(k/n), uniformly in k if, and only if, the underlying distribution function is ultimately a generalized Pareto distribution. Thus, generalized Pareto distributions yield the best rate of joint convergence of extremes.
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© 1989 Springer-Verlag Berlin Heidelberg
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Falk, M. (1989). Best Attainable Rate of Joint Convergence of Extremes. In: Hüsler, J., Reiss, RD. (eds) Extreme Value Theory. Lecture Notes in Statistics, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3634-4_1
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DOI: https://doi.org/10.1007/978-1-4612-3634-4_1
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