hill.adapt {extremefit}

Compute the extreme quantile procedure

Description

Compute the extreme quantile procedure

Usage

hill.adapt(X, weights = rep(1, length(X)), initprop = 1/10,
  gridlen = 100, r1 = 1/4, r2 = 1/20, CritVal = 10, plot = F)

Arguments

X

a numeric vector of data values.

weights

a numeric vector of weigths associated to the vector X.

initprop

the initial proportion at which we begin to test the model.

gridlen

the length of the grid for which the test is done.

r1

a proportion value of the data from the right that we skip in the test statistic.

r2

a proportion value of the data from the left that we skip in the test statistic.

CritVal

the critical value assiociated to the weights.

plot

If TRUE, the results are plotted.

Details

Given a vector of data and assiociated weights, this function compute the adaptive procedure described in Grama and Spokoiny (2008) and Durrieu et al. (2015).

We suppose that the data are in the domain of attraction of the Frechet-Pareto type. Otherwise, the procedure will not work.

Value

Xsort

the sorted vector of the data.

sortweights

the weights associated to Xsort.

wh

the weighted Hill estimator associated to X (output of the function hill).

TestingGrid

the grid used for the statistic test.

TS, TS1, TS.max, TS1.max

respectively the test statistic, the likelihood ratio test, the maximum of the test statistic and the maximum likelihood ratio test.

Paretodata

logical: if TRUE the distribution of the data is a Pareto distribution.

Paretotail

logical: if TRUE a Pareto tail was detected.

madapt

the first indice of the TestingGrid for which the test statistic exceeds the critical value.

kadapt

the adaptive indice of the threshold.

kadapt.maxlik

the maximum likelihood corresponding to the adaptive threshold in the selected testing grid.

hadapt

the adaptive weighted parameter of the Pareto distribution after the threshold.

Xadapt

the adaptive threshold.

Author(s)

Ion Grama

References

Grama, I. and Spokoiny, V. (2008). Statistics of extremes by oracle estimation. Ann. of Statist., 36, 1619-1648.

Durrieu, G. and Grama, I. and Pham, Q. and Tricot, J.- M. (2015). Nonparametric adaptive estimator of extreme conditional tail probabilities quantiles. Extremes, 18, 437-478.

Durrieu, G. and Grama, I. and Jaunatre, K. and Pham, Q.-K. and Tricot, J.-M. (2018). extremefit: A Package for Extreme Quantiles. Journal of Statistical Software, 87, 1–20.

Examples

x <- abs(rcauchy(100))
HH <- hill.adapt(x, weights=rep(1, length(x)), initprop = 0.1,
               gridlen = 100 , r1 = 0.25, r2 = 0.05, CritVal=10,plot=TRUE)
#the critical value 10 is assiociated to the rectangular kernel.
HH$Xadapt # is the adaptive threshold
HH$hadapt # is the adaptive parameter of the Pareto distribution