RobExtremes (version 1.3.0)

asvarPickands: Function to compute asymptotic variance of Pickands estimator

Description

Function asvarPickands computes the asymptotic (co)variance of a Pickands estimator at a GPD or GEVD model -- the latter with location mu known or unknown.

Usage

asvarPickands( model, alpha=2)

Value

A 2x2 matrix (resp., for mu unknown in the GEV model a 3x3 matrix); the covariance.

Arguments

model

an object of class "ScaleShapeUnion".

alpha

numeric > 1; determines the variant of the Pickands-Estimator based on matching the empirical \(a_1=1-1/\alpha\) and \(a_1=1-1/\alpha^2\) quantiles against the population counter parts. The ``classical'' Pickands Estimator is obtained for alpha=2 (GPD) resp. for alpha=1/log(2) (GEVD).

Author

Peter Ruckdeschel

Details

All terms are analytic.

References

Ruckdeschel, P. and Horbenko, N. (2013): Optimally-Robust Estimators in Generalized Pareto Models. Statistics 47(4), 762--791. DOI: 10.1080/02331888.2011.628022.

See Also

PickandsEstimator

Examples

GP <- GParetoFamily(scale=1,shape=0.7)
asvarPickands(GP)
asvarPickands(GP,alpha=2.3)
GE <- GEVFamily(loc=0,scale=1,shape=0.7)
asvarPickands(GE)
GE0 <- GEVFamilyMuUnknown(loc=0,scale=1,shape=0.7)
asvarPickands(GE0)