Minimizing the AMSE of the Hill estimator with respect to k
Gives the optimal number of upper order statistics k
for the Hill estimator by minimizing the AMSE-criterion.
dAMSE(data)
data |
vector of sample data |
The optimal number of upper order statistics 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. This number is identified by minimizing the AMSE criterion with respect to k
. The optimal number, denoted k0
here, can then be associated with the unknown threshold u
of the GPD by choosing u
as the n-k0
th upper order statistic. For more information see references.
second.order.par |
gives an estimation of the second order parameter |
k0 |
optimal number of upper order statistics, i.e. number of exceedances or data in the tail |
threshold |
the corresponding threshold |
tail.index |
the corresponding tail index |
Caeiro, J. and Gomes, M.I. (2016). Threshold selection in extreme value analysis. Extreme Value Modeling and Risk Analysis:Methids and Applications, 69–86.
data(danish) dAMSE(danish)
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