Robust extreme value analysis: the bulk matching method

Traditional extreme value analysis based on the generalised ex-
treme value (GEV) or generalised Pareto distribution (GPD) suffers
from two drawbacks: (i) Both methods are wasteful of data as only
block maxima or exceedances over a high threshold are taken into ac-
count and the bulk of the data is disregarded. (ii) Moreover, in the
GPD approach, there is no systematic way to determine the threshold
parameter. Here, all the data are fitted simultaneously using a gener-
alised exponential family model for the bulk and a GPD model for the
tail. At the threshold, the two distributions are linked together with
appropriate matching conditions. The model parameters are estimated
from the likelihood function of all the data. Also the threshold param-
eter can be determined via maximum likelihood in an outer loop. The
method is exemplified on wind speed data from an atmospheric model.