ParetoFamily {RobExtremes}

Generating function for Generalized Pareto families

Description

Generates an object of class "ParetoFamily" which represents a Pareto family.

Usage

ParetoFamily(Min = 1, shape = 0.5, trafo = NULL, start0Est = NULL,
                    withCentL2 = FALSE)

Arguments

Min

real: known/fixed threshold/location parameter

shape

positive real: shape parameter

trafo

matrix or NULL: transformation of the parameter

start0Est

startEstimator — if NULL log(2)/log(median/Min) is used

withCentL2

logical: shall L2 derivative be centered by substracting the E()? Defaults to FALSE, but higher accuracy can be achieved when set to TRUE.

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "ParetoFamily"

Author(s)

Matthias Kohl [e-mail]
Peter Ruckdeschel [e-mail]
Nataliya Horbenko [e-mail]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M., Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333-354. doi:10.1007/s10260-010-0133-0.

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

Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion: EFSBP –illustrated at scale-shape models. Metrika, 75(8), 1025–1047. doi:10.1007/s00184-011-0366-4.

See Also

L2ParamFamily-class, Pareto

Examples

(P1 <- ParetoFamily())
FisherInfo(P1)
checkL2deriv(P1)