Extreme U-statistic Pickands estimator

Given a random sample of n exceedances, the estimator returns an estimator of the shape parameter or extreme value index using a kernel of order 3, based on k largest exceedances of xdat. Note that the method does not allow for ties.

Usage

shape.osz(xdat, k, ...)

Arguments

xdat

vector of observations of length \(n\)

k

number of largest order statistics \(3 \leq k < n\).

...

additional arguments for backward compatibility

Details

The calculations are based on the recursions provided in Lemma 4.3 of Oorschot et al.

References

Oorschot, J, J. Segers and C. Zhou (2023), Tail inference using extreme U-statistics, Electronic Journal of Statistics 17(1): 1113-1159. doi:10.1214/23-EJS2129

Examples

xdat <- rgp(n = 1000, shape = 0.2)
shape.osz(xdat, k = 10)
#> [1] 0.2708725