A Location Invariant Pickands-Type Estimator
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Abstract
In this paper, the author proposes a location invariant Pickands-type estimator as the extreme index is positive. Its weak and strong convergence are proved. Asymptotical representation and strong convergence rate are derived, and the optimal choice of k_2 is found. At last simulation and comparison of this new kind of Pickands-type estimator with other known Pickands-type estimators are considered by using the adaptive algorithm.
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