Restricting to the largest fourth of the data, returns the number of exceedances that minimizes the Kolmogorov-Smirnov statistic, i.e., the maximum absolute difference between the estimated generalized Pareto and the empirical distribution of exceedances. Relative to the paper, different estimation methods are proposed.
Usage
thselect.pickands(xdat, thresh, method = c("mle", "lmom", "quartiles"))Arguments
- xdat
[numeric] vector of observations
- thresh
[numeric] vector of candidate thresholds. If missing, defaults to order statistics from the 10th to a quarter of the sample size.
- method
[string] estimation method, either the quartiles of Pickands (1975), maximum likelihood, probability weighted moments or L-moments
Value
a list with components
k0: number of exceedancesthresh0: selected threshold returned by the procedurethresh: vector of candidate thresholdsdist; vector of Kolmogorov-Smirnoff distancemethod; string for the estimation methodscale: estimated scale parameter at the chosen thresholdshape: estimated shape parameter at the chosen threshold
Note
The quartiles estimator of Pickands is robust, but very inefficient. It is provided for historical reasons.
References
James Pickands III (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3(1) 119-131, doi:10.1214/aos/1176343003