Adaptive choice of the optimal sample fraction in tail index estimation
An implementation of the minimization criterion proposed in Reiss & Thomas (2007).
RT(data, beta = 0, kmin = 2)
data |
vector of sample data |
beta |
a factor for weighting the expression below. Default is set to |
kmin |
gives a minimum value for |
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
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 |
Reiss, R.-D. and Thomas, M. (2007). Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields. Birkhauser, Boston.
data(danish) RT(danish)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.