RobExtremes-package: RobExtremes -- Optimally Robust Estimation for Extreme Value Distributions

Description

RobExtremes provides infrastructure for speeded-up optimally robust estimation (i.e., MBRE, OMSE, RMXE) for extreme value distributions, extending packages distr, distrEx, distrMod, robustbase, RobAStBase, and ROptEst.

Arguments

Distributions

Importing from packages actuar, evd, it provides S4 classes and methods for the

Generalized Extreme Value distribution (GEVD)
Generalized Pareto distribution (GPD)
Pareto distribution

Functionals for Distributions

These distributions come together with particular methods for expectations. I.e., a functional E() as in package distrEx, which as first argument takes the distribution, and, optionally, can take as second argument a function which then is used as integrand. These particular methods are available for the GPD, Pareto, Gamma, Weibull, and GEV disdribution and use integration on the quantile scale, i.e., $$\mathop{E}[X]=\int_0^1 q^X(s)\,ds$$ where $q^X$ is the quantile function of X. In addition, where they exist, we provide closed from expressions for variances, median, IQR, skewness, kurtosis.
In addition, extending estimators Sn and Qn from package robustbase, we provide functionals for Sn and Qn. A new asymmetric version of the mad, kMAD gives yet another robust scale estimator (and functional).

Models and Estimators

As to models, we provide the

GPD model (with known threshold), together with (speeded-up) optimally robust estimators, with LDEstimators (in general, and with medkMAD, medSn and medQn as particular ones) and Pickands' estimator as starting estimators.
GEVD model (with known or unknown threshold), together with (speeded-up) optimally robust estimators, with LDEstimators (see above) and Pickands' estimator as starting estimators.
Pareto model
Weibull model
Gamma model

and for each of these, we provide speeded-up optimally robust estimation (i.e., MBRE, OMSE, RMXE).
We robust (high-breakdown) starting estimators for

GPD (PickandsEstimator, medkMAD, medSn, medQn)
GEV (PickandsEstimator)
Pareto (Cramér-von-Mises-Minimum-Distance-Estimator)
Weibull (the quantile based estimator of Boudt/Caliskan/Croux)
Gamma (Cramér-von-Mises-Minimum-Distance-Estimator)

For all these families, of course, MLEs and Minimum-Distance-Estimators are also available through package "distrMod".

Diagnostics

We bridge to the diagnostics provided by package "ismev", i.e. our return objects can be plugged into the diagnostics of this package.
We have the usual diagnostic plots from package "RobAStBase", i.e.

Outylingness plots outlyingPlotIC
IC plots plot
Information plots via infoPlot
IC comparison plots via comparePlot
Cniperpoint plots (from package "ROptEst") via CniperPointPlot

but also (adopted from package "distrMod")

qqplots (with confidence bands) via qqplot
returnlevel plots via returnlevelplot

Starting Point

As a starting point you may look at the included script "RobFitsAtRealData.R" in the scripts folder of the package, accessible by file.path(system.file(package="RobExtremes"), "scripts/RobFitsAtRealData.R").

Classes


[*]: there is a generating function with the same name in RobExtremes
[**]:  generating function from distrMod, but with (speeded-up)
       opt.rob-estimators in RobExtremes
##########################
Distribution Classes
##########################
"Distribution" (from distr)
|>"UnivariateDistribution" (from distr)
|>|>"AbscontDistribution" (from distr)
|>|>|>"Gumbel"    [*]
|>|>|>"Pareto"    [*]
|>|>|>"GPareto"   [*]
|>|>|>"GEVD"      [*]
##########################
Parameter Classes
##########################
"OptionalParameter" (from distr)
|>"Parameter" (from distr)
|>|>"GumbelParameter"
|>|>"ParetoParameter"
|>|>"GEVDParameter"
|>|>"GParetoParameter"
##########################
ProbFamily classes
##########################
slots: [<name>(<class>)]
"ProbFamily"                                  (from distrMod)
|>"ParamFamily"                               (from distrMod)
|>|>"L2ParamFamily"                           (from distrMod)
|>|>|>"L2GroupParamFamily"                    (from distrMod)
|>|>|>|>"ParetoFamily"                  [*]
|>|>|>|>"L2ScaleShapeUnion"                   (from distrMod)
|>|>|>|>|>"GammaFamily"                 [**]
|>|>|>|>|>"GParetoFamily"               [*]
|>|>|>|>|>"GEVFamily"                   [*]
|>|>|>|>|>"WeibullFamily"               [**]
|>|>|>|>"L2LocationScaleUnion"  /VIRTUAL/     (from distrMod)
|>|>|>|>|>"L2LocationFamily"                  (from distrMod)
|>|>|>|>|>|>"GumbelLocationFamily"      [*]
|>|>|>|>"L2LocScaleShapeUnion"  /VIRTUAL/     (from distrMod)
|>|>|>|>|>"GEVFamilyMuUnknown"          [*]

Functions


LDEstimator     Estimators for scale-shape models based on
                location and dispersion
medSn                    loc=median disp=Sn
medQn                    loc=median disp=Qn
medkMAD                  loc=median disp=kMAD
asvarMedkMAD               [asy. variance to MedkMADE]
PickandsEstimator        PickandsEstimator
asvarPickands              [asy. variance to PickandsE]
QuantileBCCEstimator     Quantile based estimator for the Weibull distribution
asvarQBCC                  [asy. variance to QuantileBCCE]

Generating Functions


Distribution Classes
Gumbel                  Generating function for Gumbel-class
GEVD                    Generating function for GEVD-class
GPareto                 Generating function for GPareto-class
Pareto                  Generating function for Pareto-class
L2Param Families
ParetoFamily            Generating function for ParetoFamily-class
GParetoFamily           Generating function for GParetoFamily-class
GEVFamily               Generating function for GEVFamily-class
WeibullFamily           Generating function for WeibullFamily-class

Methods


Functionals:
E                       Generic function for the computation of
                        (conditional) expectations
var                     Generic functions for the computation of functionals
IQR                     Generic functions for the computation of functionals
median                  Generic functions for the computation of functionals
skewness                Generic functions for the computation of functionals
kurtosis                Generic functions for the computation of functionals
Sn                      Generic function for the computation of (conditional)
                        expectations
Qn                      Generic functions for the computation of functionals

Constants


EULERMASCHERONICONSTANT
APERYCONSTANT

Acknowledgement

This package is joint work by Peter Ruckdeschel, Matthias Kohl, and Nataliya Horbenko (whose PhD thesis went into this package to a large extent), with contributions by Dasha Pupashenko, Misha Pupashenko, Gerald Kroisandt, Eugen Massini, Sascha Desmettre, and Bernhard Spangl, in the framework of project "Robust Risk Estimation" (2011-2016) funded by Volkswagen foundation (and gratefully ackknowledged). Thanks also goes to the maintainers of CRAN, in particully to Uwe Ligges who greatly helped us with finding an appropriate way to store the database of interpolating functions which allow the speed up -- this is now package RobAStRDA on CRAN.

Author

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de, and
Nataliya Horbenko nhorbenko@gmail.com,
Maintainer: Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Start-up-Banner

You may suppress the start-up banner/message completely by setting options("StartupBanner"="off") somewhere before loading this package by library or require in your R-code / R-session. If option "StartupBanner" is not defined (default) or setting options("StartupBanner"=NULL) or options("StartupBanner"="complete") the complete start-up banner is displayed. For any other value of option "StartupBanner" (i.e., not in c(NULL,"off","complete")) only the version information is displayed. The same can be achieved by wrapping the library or require call into either suppressStartupMessages() or onlytypeStartupMessages(.,atypes="version"). As for general packageStartupMessage's, you may also suppress all the start-up banner by wrapping the library or require call into suppressPackageStartupMessages() from startupmsg-version 0.5 on.

Package versions

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the RobAStXXX family as a whole in order to ease updating "depends" information.

Details

Package:	RobExtremes
Version:	1.3.2
Date:	2025-01-15
Title:	Optimally Robust Estimation for Extreme Value Distributions
Description:	Optimally robust estimation for extreme value distributions using S4 classes and methods
	(based on packages distr, distrEx, distrMod, RobAStBase, and ROptEst).
Depends:	R(>= 3.4), methods, distrMod(>= 2.8.0), ROptEst(>= 1.2.0), robustbase, evd
Suggests:	RUnit(>= 0.4.26), ismev(>= 1.39)
Imports:	RobAStRDA, distr, distrEx(>= 2.8.0), RandVar, RobAStBase(>= 1.2.0), startupmsg(>=1.0.0), actuar
Authors:	Bernhard Spangl [contributed smoothed grid values of the Lagrange multipliers]
	Sascha Desmettre [contributed smoothed grid values of the Lagrange multipliers]
	Eugen Massini [contributed an interactive smoothing routine for smoothing the
	Lagrange multipliers and smoothed grid values of the Lagrange multipliers]
	Daria Pupashenko [contributed MDE-estimation for GEV distribution in the framework of
	her PhD thesis 2011--14]
	Gerald Kroisandt [contributed testing routines]
	Nataliya Horbenko ["aut","cph"]
	Matthias Kohl ["aut", "cph"]
	Peter Ruckdeschel ["cre", "aut", "cph"],
Contact:	peter.ruckdeschel@uni-oldenburg.de
ByteCompile:	yes
LazyLoad:	yes
License:	LGPL-3
URL:	https://r-forge.r-project.org/projects/robast/
Encoding:	UTF-8
VCS/SVNRevision:	1332

References

Horbenko, N., Ruckdeschel, P., and Bae, T. (2011): Robust Estimation of Operational Risk. Journal of Operational Risk 6(2), 3-30.
M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.
M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 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").
Ruckdeschel, P., Kohl, M., Stabla, T., and Camphausen, F. (2006): S4 Classes for Distributions, R News, 6(2), 2-6. https://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf.
A vignette for packages distr, distrSim, distrTEst, and RobExtremes is included into the mere documentation package distrDoc and may be called by require("distrDoc");vignette("distr"). A homepage to this package is available under http://robast.r-forge.r-project.org/.