RT {tea}

Adaptive choice of the optimal sample fraction in tail index estimation

Description

An implementation of the minimization criterion proposed in Reiss & Thomas (2007).

Usage

RT(data, beta = 0, kmin = 2)

Arguments

data

vector of sample data

beta

a factor for weighting the expression below. Default is set to beta=0

kmin

gives a minimum value for k. Default ist set to kmin=2

Details

The procedure proposed in Reiss & Thomas (2007) chooses the lowest upper order statistic k to minimize the expression 1/k sum_i=1^k i^beta |gamma_i-median(gamma_1,...,gamma_k)| or an alternative of that by replacing the absolute deviation with a squared deviation and the median just with gamma_k, where gamma denotes the Hill estimator

Value

k0

optimal number of upper order statistics, i.e. number of exceedances or data in the tail for both metrics, i.e. the absolute and squared deviation.

threshold

the corresponding thresholds.

tail.index

the corresponding tail indices

References

Reiss, R.-D. and Thomas, M. (2007). Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields. Birkhauser, Boston.

Examples

data(danish)
RT(danish)