Generates an object of class "GParetoFamily"
which
represents a Generalized Pareto family.
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)
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
medkMADhybr
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).
logical: only used internally in kStepEstimator
; do not change this.
Object of class "GParetoFamily"
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. (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.
L2ParamFamily-class
, '>GPareto
# NOT RUN {
(G1 <- GParetoFamily())
FisherInfo(G1)
checkL2deriv(G1)
# }
Run the code above in your browser using DataLab