## Robust estimations for the tail index of Weibull-type distribution

### Abstract

Based on suitable left-truncated or censored data, two flexible classes of $M$-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with $\sqrt {n}$-rate of convergence is obtained. Its robustness is discussed via its asymptotic relative efficiency and influence function. It is further demonstrated by a small scale of simulations and an empirical study on CRIX

Topics: Mathematics - Statistics Theory
Year: 2018
OAI identifier: oai:arXiv.org:1809.01317

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