Minimax Risk Bounds in Extreme Value Theory
نویسنده
چکیده
Asymptotic minimax estimators of a positive extreme value index under zero-one loss are investigated in the classical i.i.d. setup. To this end, we prove the weak convergence of suitable local experiments with Pareto distributions as center of localization to a white noise model, which was previously studied in the context of nonparametric local density estimation and regression. From this result we derive upper and lower bounds on the asymptotic minimax risk in the local and in certain global models as well. Finally, the implications for xed-length conndence intervals are discussed. In particular, asymptotic conndence intervals with almost minimal length are constructed, while the popular Hill estimator is shown to yield a little longer conndence intervals.
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