GParetoFamily: Generating function for Generalized Pareto families

In RobExtremes: Optimally Robust Estimation for Extreme Value Distributions

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)

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 Xi, the expression 1+shape(Xi-loc)/scale must be positive, which in principle could be attacked by a single outlier. Hence for sample size n we allow for eps n violations, interpreting the violations as outliers. Here eps = 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.

Details

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

Value

Object of class "GParetoFamily"

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.

M.~Kohl, P. Ruckdeschel, H.~Rieder (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354.

Ruckdeschel, P. and Horbenko, N. (2011): Optimally-Robust Estimators in Generalized Pareto Models. ArXiv 1005.1476. To appear at Statistics. 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.

See Also

L2ParamFamily-class, GPareto

Examples

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

RobExtremes documentation built on May 2, 2019, 3:44 p.m.