tea (version 1.1)

dAMSE: Minimizing the AMSE of the Hill estimator with respect to k

Description

Gives the optimal number of upper order statistics k for the Hill estimator by minimizing the AMSE-criterion.

Usage

dAMSE(data)

Arguments

data

vector of sample data

Value

second.order.par

gives an estimation of the second order parameter beta and 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 index

Details

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.

References

Caeiro, J. and Gomes, M.I. (2016). Threshold selection in extreme value analysis. Extreme Value Modeling and Risk Analysis:Methids and Applications, 69--86.

Examples

# NOT RUN {
data(danish)
dAMSE(danish)
# }