Minimizing the AMSE of the Hill estimator with respect to k
An Implementation of the procedure proposed in Hall & Welsh (1985) for obtaining the optimal number of upper order statistics k for the Hill estimator by minimizing the AMSE-criterion.
HW(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-k0th 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 |
Hall, P. and Welsh, A.H. (1985). Adaptive estimates of parameters of regular variation. The Annals of Statistics, 13(1), 331–341.
data(danish) HW(danish)
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