asvarPickands {RobExtremes}

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)

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).

Details

All terms are analytic.

Value

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

Author(s)

Peter Ruckdeschel [e-mail]

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)