extES: Extreme Expected Shortfall estimation

In AntoineUC/Expectrem: Bias-reduced estimation of extreme value index and extreme quantiles, expectiles and Expected Shortfalls

Extreme Expected Shortfall estimation

Description

This function computes several estimators for extreme Expected Shortfalls.

Usage

extES(X,k,tau,estim="Moment",method="direct",ci.level=0.95,n.bootstrap=10000)

Arguments

X	Data vector.
k	A vector of number of upper order statistics.
tau	Numeric (extreme) probability with value in [0,1].
estim	ES estimator used : Moment estimator ("Moment", default) tailored for all domains of attraction, or Weissman/Hill estimator ("Hill", default), only suitable for heavy-tailed distribution (positive tail index).
method	Direct ("direct", default) or indirect ("indirect") estimator.
ci.level	Confidence level. Default: 0.95.
n.bootstrap	Size of the bootstrap sample simulated (only if method="direct" and estim="Moment", default 10,000).

Value

Lower_bound	Lower bound of the confidence interval.
Point_estimate	Expected Shortfall estimate.
Upper_bound	Upper bound of the confidence interval.

Author(s)

Antoine Usseglio-Carleve

References

Daouia, A., Stupfler, G. & Usseglio-Carleve, A. (2024). A unified framework for extreme Expected Shortfall inference.

AntoineUC/Expectrem documentation built on Feb. 14, 2025, 11:22 a.m.