Description Usage Arguments Details Value References Examples
An Implementation of the procedure proposed in Hall (1990) for selecting the optimal sample fraction in tail index estimation
1 |
data |
vector of sample data |
B |
number of Bootstrap replications |
epsilon |
gives the amount of the first resampling size |
kaux |
tuning parameter for the hill estimator |
The Bootstrap procedure simulates the AMSE criterion of the Hill estimator. The unknown theoretical parameter of the inverse tail index gamma
is replaced by a consistent estimation using a tuning parameter kaux
for the Hill estimator. 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-k0
th upper order statistic. For more information see references.
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. (1990). Using the Bootstrap to Estimate Mean Squared Error and Select Smoothing Parameter in Nonparametric Problems. Journal of Multivariate Analysis, 32, 177–203.
1 2 |
Loading required package: eva
$k0
[1] 80
$threshold
[1] 12.52319
$tail.index
[1] 1.705818
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.