danielsson {tea} | R Documentation |
A Double Bootstrap Procedure for Choosing the Optimal Sample Fraction
Description
An Implementation of the procedure proposed in Danielsson et al. (2001) for selecting the optimal sample fraction in tail index estimation.
Usage
danielsson(data, B = 500, epsilon = 0.9)
Arguments
data |
vector of sample data |
B |
number of Bootstrap replications |
epsilon |
gives the amount of the first resampling size |
Details
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-k0
th upper order statistic. For more information see references.
Value
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 |
References
Danielsson, J. and Haan, L. and Peng, L. and Vries, C.G. (2001). Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate analysis, 2, 226-248.
Examples
data=rexp(100)
danielsson(data, B=200)