Abstract
In this paper, we build a two-step estimator \(\hat{\gamma}_{\rm STEP}\), which satisfies \(\sqrt{k}(\hat{\gamma}_{\rm STEP}-\hat{\gamma}_{ML})\stackrel{P}{\rightarrow} 0\), where \(\hat{\gamma}_{ML}\) is the well-known maximum likelihood estimator of the extreme value index. Since the two-step estimator \(\hat{\gamma}_{\rm STEP}\) can be calculated easily as a function of the observations, it is much simpler to use in practice. By properly choosing the first step estimator, such as the Pickands estimator, we can even get a shift and scale invariant estimator with the above property.
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The author thanks Laurens de Haan for motivating this work and giving helpful comments. The author also thanks two anonymous referees for their useful comments.
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Zhou, C. A two-step estimator of the extreme value index. Extremes 11, 281–302 (2008). https://doi.org/10.1007/s10687-008-0058-2
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DOI: https://doi.org/10.1007/s10687-008-0058-2