ParetoFamily: 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)

Value

Object of class "ParetoFamily"

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.

Author

Matthias Kohl Matthias.Kohl@stamats.de
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Nataliya Horbenko nhorbenko@gmail.com

Details

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

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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1007/s00184-011-0366-4").

Examples

Run this code

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

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