RobExtremes (version 1.2.0)

PickandsEstimator: Function to compute Pickands estimates for the GPD and GEVD

Description

Function PickandsEstimator computes Pickands estimator (for the GPD and GEVD) at real data and returns an object of class Estimate.

Usage

PickandsEstimator(x, ParamFamily=GParetoFamily(), alpha=2,
            name, Infos, nuis.idx = NULL,
            trafo = NULL, fixed = NULL, na.rm = TRUE,
            ...)
.PickandsEstimator(x, alpha=2, GPD.l = TRUE)

Arguments

x

(empirical) data

alpha

numeric \(> 1\); determines the variant of the Pickands-Estimator based on matching the empirical quantiles to levels \(a_1=1-1/\alpha\) and \(a_2=1-1/\alpha^2\) (in the GPD case) resp. \(a_1=\exp(-1/\alpha)\) and \(a_1=\exp(-1/\alpha^2)\) (in the GEVD case) against the population counter parts. The ''classical'' Pickands Estimator building up on the median is obtained for alpha=2 for the GPD and for alpha = 1/log(2) for the GEVD. If alpha is missing we set it to the optimal value (see note below).

ParamFamily

an object of class "GParetoFamily" or "GEVFamily".

name

optional name for estimator.

Infos

character: optional informations about estimator

nuis.idx

optionally the indices of the estimate belonging to nuisance parameter

fixed

optionally (numeric) the fixed part of the parameter

trafo

an object of class MatrixorFunction -- a transformation for the main parameter

na.rm

logical: if TRUE, the estimator is evaluated at complete.cases(x).

…

not yet used.

GPD.l

logical: if TRUE the variant for GPD is used, else for GEVD.

Value

.PickandsEstimator

A numeric vector of length 2 with components named scale and shape.

PickandsEstimator

An object of S4-class "Estimate".

Details

The actual work is done in .PickandsEstimator. The wrapper PickandsEstimator pre-treats the data, and constructs a respective Estimate object.

References

P. Ruckdeschel, N. Horbenko (2012): Yet another breakdown point notion: EFSBP --illustrated at scale-shape models. Metrika, 75(8), 1025--1047.

J. Pickands (1975): Statistical inference using extreme order statistics. Ann. Stat. 3(1), 119--131.

See Also

ParamFamily-class, ParamFamily, Estimate-class

Examples

# NOT RUN {
## (empirical) Data
set.seed(123)
x <- rgpd(50, scale = 0.5, shape = 3)
y <- rgev(50, scale = 0.5, shape = 3)
## parametric family of probability measures
P <- GParetoFamily(scale = 1, shape = 2)
G <- GEVFamily(scale = 1, shape = 2)
##
PickandsEstimator(x = x, ParamFamily = P)
PickandsEstimator(x = y, ParamFamily = G)
# }