EBTailIndex {ExtremeRisks} | R Documentation |
Expectile Based Tail Index Estimation
Description
Computes a point estimate of the tail index based on the Expectile Based (EB) estimator.
Usage
EBTailIndex(data, tau, est=NULL)
Arguments
data |
A vector of |
tau |
A real in |
est |
A real specifying the estimate of the expectile at the intermediate level |
Details
For a dataset data
of sample size , the tail index
of its (marginal) distribution is estimated using the EB estimator:
,
where is the empirical survival function of the observations,
is an estimate of the
-th expectile.
The observations can be either independent or temporal dependent. See Padoan and Stupfler (2020) and Daouia et al. (2018) for details.
The so-called intermediate level
tau
oris a sequence of positive reals such that
as
. Practically,
is the ratio between the empirical mean distance of the
-th expectile from the smaller observations and the empirical mean distance of of the
-th expectile from all the observations. An estimate of
-th expectile is computed and used in turn to estimate
.
The value
est
, if provided, is meant to be an esitmate of the-th expectile which is used to estimate
. On the contrary, if
est=NULL
, then the routineEBTailIndex
estimate first the-th expectile expectile and then use it to estimate
.
Value
An estimate of the tain index .
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, http://mypage.unibocconi.it/simonepadoan/; Gilles Stupfler, gilles.stupfler@ensai.fr, http://ensai.fr/en/equipe/stupfler-gilles/
References
Padoan A.S. and Stupfler, G. (2020). Extreme expectile estimation for heavy-tailed time series. arXiv e-prints arXiv:2004.04078, https://arxiv.org/abs/2004.04078.
Daouia, A., Girard, S. and Stupfler, G. (2018). Estimation of tail risk based on extreme expectiles. Journal of the Royal Statistical Society: Series B, 80, 263-292.
See Also
HTailIndex, MomTailIndex, MLTailIndex,
Examples
# Tail index estimation based on the Expectile based estimator obtained with data
# simulated from an AR(1) with 1-dimensional Student-t distributed innovations
tsDist <- "studentT"
tsType <- "AR"
# parameter setting
corr <- 0.8
df <- 3
par <- c(corr, df)
# Big- small-blocks setting
bigBlock <- 65
smallblock <- 15
# Intermediate level (or sample tail probability 1-tau)
tau <- 0.97
# sample size
ndata <- 2500
# Simulates a sample from an AR(1) model with Student-t innovations
data <- rtimeseries(ndata, tsDist, tsType, par)
# tail index estimation
gammaHat <- EBTailIndex(data, tau)
gammaHat