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Risks 2018, 6(4), 119; https://doi.org/10.3390/risks6040119

Robust Estimations for the Tail Index of Weibull-Type Distribution

1,†
and
1,2,†,*
1
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2
Department of Actuarial Science, University of Lausanne, Chamberonne, 1015 Lausanne, Switzerland
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 1 September 2018 / Revised: 30 September 2018 / Accepted: 9 October 2018 / Published: 11 October 2018
(This article belongs to the Special Issue Heavy-Tail Phenomena in Insurance, Finance, and Other Related Fields)
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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 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. View Full-Text
Keywords: robust; Weibull tail coefficient; influence function; asymptotic relative efficiency; CRIX robust; Weibull tail coefficient; influence function; asymptotic relative efficiency; CRIX
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Gong, C.; Ling, C. Robust Estimations for the Tail Index of Weibull-Type Distribution. Risks 2018, 6, 119.

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