DK {tea}

A Bias-based procedure for Choosing the Optimal Sample Fraction

Description

An Implementation of the procedure proposed in Drees & Kaufmann (1998) for selecting the optimal sample fraction in tail index estimation.

Usage

DK(data, r = 1)

Arguments

data

vector of sample data

r

tuning parameter for the stopping criterion. default is set to 1. Change only if recommended by the output.

Details

The procedure proposed in Drees & Kaufmann (1998) is based on bias reduction. A stopping criterion with respect to k is implemented to find the optimal tail fraction, i.e. 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. If the above mentioned stopping criterion exceedes a certain value r, the bias of the assumed extreme model has become prominent and therefore k should not be chosen higher. For more information see references.

Value

second.order.par

gives an estimation of the second order parameter rho.

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

References

Drees, H. and Kaufmann, E. (1998). Selecting the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and their Applications, 75(2), 149–172.

Examples

data(danish)
DK(danish)