An Implementation of the procedure proposed in Gomes et al. (2012) and Caeiro et al. (2016) for selecting the optimal sample fraction in tail index estimation.
gomes(data, B = 1000, epsilon = 0.995)vector of sample data
number of Bootstrap replications
gives the amount of the first resampling size n1 by choosing n1 = n^epsilon. Default is set to epsilon=0.995
gives an estimation of the second order parameter rho.
optimal number of upper order statistics, i.e. number of exceedances or data in the tail
the corresponding threshold
the corresponding tail
The Double Bootstrap procedure simulates the AMSE criterion of the Hill estimator using an auxiliary statistic. Minimizing this statistic gives a consistent estimator of the sample fraction k/n with k the optimal number of upper order statistics. This number, denoted k0 here, is equivalent to the number of extreme values or, if you wish, the number of exceedances in the context of a POT-model like the generalized Pareto distribution. k0 can then be associated with the unknown threshold u of the GPD by choosing u as the n-k0th upper order statistic. For more information see references.
Gomes, M.I. and Figueiredo, F. and Neves, M.M. (2012). Adaptive estimation of heavy right tails: resampling-based methods in action. Extremes, 15, 463--489.
Caeiro, F. and Gomes, I. (2016). Threshold selection in extreme value analysis. Extreme Value Modeling and Risk Analysis: Methods and Applications, 69--86.
# NOT RUN {
data(danish)
gomes(danish)
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