Rates of uniform convergence of extreme order statistics
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Bounds for the convergence uniformly over all Borel sets of the largest order statistic as well as of the joint distribution of extremes are established which reveal in which way these rates are determined by the distance of the underlying density from the density of the corresponding generalized Pareto distribution.
The results are highlighted by several examples among which there is a bound for the rate at which the joint distribution of thek largest order statistics from a normal distribution converges uniformly to its limit.
Key words and phrasesGeneralized Pareto distribution uniform distance joint distribution of extremes normal extremes
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- Falk, M. (1984).Uniform Convergence of Extreme Order Statistics I, Preprint 122, University of Siegen.Google Scholar
- Ikeda, S. and Matsunawa, T. (1976). Uniform asymptotic distribution of extremes, inEssays in Probability and Statistics (eds. S. Ikeda et al.), Shinko Tsusho, Tokyo, 419–432.Google Scholar
- Reiss, R.-D. (1977). Asymptotic theory for order statistics,Lecture notes, University of Freiburg.Google Scholar
- Reiss, R.-D. (1984).Statistical Inference Using Approximate Extreme Value Models, Preprint 124, University of Siegen.Google Scholar