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A Bahadur-Kiefer Theorem beyond the Largest Observation

  • Mathematics


It is shown that under natural extreme-value conditions a distributional Bahadur-Kiefer theorem holds in a point lying outside the sample. The limiting distribution is degenerate if the extreme-value index is equal to one; the proper refinement for that case is also established. In both cases the limiting distribition is chi-square with one degree of freedom.

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