Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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GENERALIZING THE REFINED PICKANDS ESTIMATOR OF THE EXTREME VALUE INDEX

  • Yun, Seok-Hoon (Department of Applied Statistics, University of Suwon)
  • Published : 2004.09.01
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Abstract

In this paper we generalize and improve the refined Pickands estimator of Drees (1995) for the extreme value index. The finite-sample performance of the refined Pickands estimator is not good particularly when the sample size n is small. For each fixed k = 1,2,..., a new estimator is defined by a convex combination of k different generalized Pickands estimators and its asymptotic normality is established. Optimal weights defining the estimator are also determined to minimize the asymptotic variance of the estimator. Finally, letting k depend upon n, we see that the resulting estimator has a better finite-sample behavior as well as a better asymptotic efficiency than the refined Pickands estimator.

Keywords

References

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