• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.339-351
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• 2004

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.