HW {tea}

Minimizing the AMSE of the Hill estimator with respect to k

Description

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.

Usage

HW(data)

Arguments

data

vector of sample data

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.

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 index

References

Hall, P. and Welsh, A.H. (1985). Adaptive estimates of parameters of regular variation. The Annals of Statistics, 13(1), 331–341.

Examples

data(danish)
HW(danish)