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Weak Convergence of the Hill Estimator Process

In: Extreme Value Theory and Applications

Author

Listed:
  • David M. Mason

    (University of Delaware, Department of Mathematical Sciences)

  • Tatyana S. Turova

    (Russian Academy of Sciences Puschino, Institute of Mathematical Problems of Biology)

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.

Suggested Citation

  • David M. Mason & Tatyana S. Turova, 1994. "Weak Convergence of the Hill Estimator Process," Springer Books, in: Janos Galambos & James Lechner & Emil Simiu (ed.), Extreme Value Theory and Applications, pages 419-431, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3638-9_25
    DOI: 10.1007/978-1-4613-3638-9_25
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