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Using a bootstrap method to choose the sample fraction in tail index estimation. (English) Zbl 0976.62044

Summary: Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e., the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two-step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the asymptotic mean-squared error. Unlike previous methods, prior knowledge of the second-order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications.

MSC:

62G32 Statistics of extreme values; tail inference
62G20 Asymptotic properties of nonparametric inference
62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods
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