Extreme value statistics for censored data with heavy tails under competing risks. (English) Zbl 1401.62076
Summary: This paper addresses the problem of estimating, from randomly censored data subject to competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in a heavy-tail framework. Asymptotic normality of the proposed estimator is established. This estimator has the form of an Aalen-Johansen integral and is the first estimator proposed in this context. Estimation of extreme quantiles of the cumulative incidence function is then addressed as a consequence. A small simulation study exhibits the performances for finite samples.
MSC:
| 62G32 | Statistics of extreme values; tail inference |
| 62N02 | Estimation in survival analysis and censored data |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
extreme value index; tail inference; random censoring; competing risks; Aalen-Johansen estimatorReferences:
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