GEVFamily: Generating function for families of Generalized Extreme Value...

In RobExtremes: Optimally Robust Estimation for Extreme Value Distributions

Generating function for families of Generalized Extreme Value distributions

Description

Generates an object of class "GEVFamily" which represents a Generalized EV family.

Usage

GEVFamily(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, ..withWarningGEV = TRUE)

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 PickandsEstimator 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). We have seen cases though, where the use of the then employed PickandsEstimator was drastically misleading and subsequently led to bad estimates where it is used as starting value; so where feasible it is a good idea to also try argument withMDE=TRUE for control purposes.
..ignoreTrafo	logical: only used internally in kStepEstimator; do not change this.
..withWarningGEV	logical: shall warnings be issued if shape is large?

Details

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

Value

Object of class "GEVFamily"

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00184-011-0366-4")}.

See Also

L2ParamFamily-class, GPareto

Examples

(G1 <- GEVFamily())
FisherInfo(G1)
checkL2deriv(G1)

RobExtremes documentation built on Jan. 12, 2025, 3:02 a.m.