Extreme value statistics for censored data with heavy tails under competing risks

Abstract

This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case. Asymptotic normality of the proposed estimator (which has the form of an Aalen-Johansen integral, and is the first estimator proposed in this context) is established. A small simulation study exhibits its performances for finite samples. Estimation of extreme quantiles of the cumulative incidence function is also addressed.

Improving the causal treatment effect estimation with propensity scores by the bootstrap

“…We also note that we adopted a uniform censoring with administratively known in advance as in ERSD data. In other real settings, censoring can be a random non-administrative with no pre-specified end point (Worms and Worms 2018;Stupfler 2019). Table 2 of the Supplemental Appendix shows simulation results obtained with and without administrative censoring.…”

Functional kernel estimation of the conditional extreme value index under random right censoring

“…Beside, Stupfler (2016) investigated the conditional estimation of the extreme value index under random censoring for all domain of attraction. While Worms and Worms (2018) proposed estimator of the extreme value index by considering heavy tailed lifetime data under random censoring and competing risks, using the Aalen-Johansen estimator of the cumulative incidence function. Beirlant et al(2019) introduced a new class of estimator which generalized the proposed estimator of Worms and Worms (2014) and Beirlant et al(2018) Some important literature is devoted to the estimation of the conditional quantile of a scalar response given a functional covariate.…”

Estimation of extremes for heavy-tailed and light-tailed distributions in the presence of random censoring

“…Worms and Worms (2014), Beirlant et al (2019) and Worms and Worms (2015) proposed a more survival analysis-oriented approach, the first two being restricted to the heavy tail case. Worms and Worms (2018) extended this survival analysis approach to competing risks. The Weibull-tail class of distributions is studied in .…”