tindexp: Proportionality tail index estimator

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

Proportionality tail index estimator

Description

This function computes the proportionality estimator of the extreme value index.

Usage

tindexp(X, k="kopt", br = FALSE)

Arguments

X	Data vector.
k	A vector of number of upper order statistics. Default: optimal k given in Girard et al. (2020).
br	Bias-reduced version if TRUE. Default: FALSE.

Details

This estimator is defined as 1/(1+Fbar(X,e(X,1-k/n))/(k/n)), where Fbar is the empirical c.s.f., and e(X,1-k/n) the empirical expectile of level 1-k/n.

Value

A vector of k estimates of the tail index.

Author(s)

Antoine Usseglio-Carleve

References

Girard, S., Stupfler, G., and Usseglio-Carleve, A. (2019). Nonparametric extreme conditional expectile estimation, preprint. https://hal.archives-ouvertes.fr/hal-02114255. Girard, S., Stupfler, G., and Usseglio-Carleve, A. (2020). On second-order automatic bias reduction for extreme expectile estimation, preprint.

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