Weak Convergence of the Hill Estimator Process

David M. Mason and Tatyana S. Turova
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David M. Mason: University of Delaware, Department of Mathematical Sciences
Tatyana S. Turova: Russian Academy of Sciences Puschino, Institute of Mathematical Problems of Biology

A chapter in Extreme Value Theory and Applications, 1994, pp 419-431 from Springer

Abstract: Abstract Let X 1 X 2,…, be a sequence of nonnegative i. i. d. random variables and for each n ≥ 1 let X 1, n ≤… ≤ Xn, n denote the order statistics based on the first n of these X’s. The Hill estimator is the sum of extreme values Σi≤kn )/k n , where k n → ∞ and k/ n →0, as n→ ∞. A weak convergence result is established for a process motivated by the Hill estimator, which we call the Hill estimator process.

Date: 1994
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DOI: 10.1007/978-1-4613-3638-9_25

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