RobExtremes (version 1.3.0)

GParetoFamily: Generating function for Generalized Pareto families

Description

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

Usage

GParetoFamily(loc = 0, scale = 1, shape = 0.5, of.interest = c("scale", "shape"),
       p = NULL, N = NULL, trafo = NULL, start0Est = NULL, withPos = TRUE,
       secLevel = 0.7,  withCentL2 = FALSE, withL2derivDistr  = FALSE,
       withMDE = FALSE, ..ignoreTrafo = FALSE)

Value

Object of class "GParetoFamily"

Arguments

loc

real: known/fixed threshold/location parameter

scale

positive real: scale parameter

shape

positive real: shape parameter

of.interest

character: which parameters, transformations are of interest.
possibilites are: "scale", "shape", "quantile", "expected loss", "expected shortfall"; a maximum number of two of these may be selected

p

real or NULL: probability needed for quantile and expected shortfall

N

real or NULL: expected frequency for expected loss

trafo

matrix or NULL: transformation of the parameter

start0Est

startEstimator --- if NULL medkMADhybr is used

withPos

logical of length 1: Is shape restricted to positive values?

secLevel

a numeric of length 1: In the ideal GEV model, for each observastion \(X_i\), the expression \(1+\frac{{\rm shape}(X_i-{\rm loc})}{{\rm scale}}\) must be positive, which in principle could be attacked by a single outlier. Hence for sample size \(n\) we allow for \(\varepsilon n\) violations, interpreting the violations as outliers. Here \(\varepsilon = {\tt secLevel}/\sqrt{n}\).

withCentL2

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

withL2derivDistr

logical: shall the distribution of the L2 derivative be computed? Defaults to FALSE (to speed up computations).

withMDE

logical: should Minimum Distance Estimators be used to find a good starting value for the parameter search? Defaults to FALSE (to speed up computations).

..ignoreTrafo

logical: only used internally in kStepEstimator; do not change this.

Author

Matthias Kohl
Peter Ruckdeschel
Nataliya Horbenko

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").

See Also

L2ParamFamily-class, GPareto

Examples

(G1 <- GParetoFamily())
FisherInfo(G1)
checkL2deriv(G1)