Generates an object of class "GEVFamily"
which
represents a Generalized EV family.
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)
real: known/fixed threshold/location parameter
positive real: scale parameter
positive real: shape parameter
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
real or NULL: probability needed for quantile and expected shortfall
real or NULL: expected frequency for expected loss
matrix or NULL: transformation of the parameter
startEstimator --- if NULL
PickandsEstimator
is used
logical of length 1: Is shape restricted to positive values?
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 \(\varepsilon = {\tt secLevel}/\sqrt{n}\).
logical: shall L2 derivative be centered by substracting
the E()? Defaults to FALSE
, but higher accuracy can be achieved
when set to TRUE
.
logical: shall the distribution of the L2 derivative
be computed? Defaults to FALSE
(to speed up computations).
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.
logical: only used internally in kStepEstimator
; do not change this.
logical: shall warnings be issued if shape is large?
Object of class "GEVFamily"
The slots of the corresponding L2 differentiable parameteric family are filled.
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. (2012): Yet another breakdown point notion: EFSBP --illustrated at scale-shape models. Metrika, 75(8), 1025--1047.
L2ParamFamily-class
, '>GPareto
# NOT RUN {
(G1 <- GEVFamily())
FisherInfo(G1)
checkL2deriv(G1)
# }
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