arXiv subjects

Rym Worms

Publications and source records attributed to Rym Worms.

5 recordsLinked to original sources

arXiv2018

Estimation of the extreme value index in a censorship framework: asymptotic and finite sample behaviour

We revisit the estimation of the extreme value index for randomly censored data from a heavy tailed distribution. We introduce a new class of estimators which encompasses earlier proposals given in Worms and Worms (2014) and Beirlant et al. (2018), which were shown to have good bias properties compared with the pseudo maximum likelihood estimator proposed in Beirlant et al. (2007) and Einmahl et al. (2008). However the asymptotic normality of the type of estimators first proposed in Worms and Worms (2014) was still lacking, in the random threshold case. We derive an asymptotic representation and the asymptotic normality of the larger class of estimators and consider their finite sample behaviour. Special attention is paid to the case of heavy censoring, i.e. where the amount of censoring in the tail is at least 50\%. We obtain the asymptotic normality with a classical $\sqrt{k}$ rate where $k$ denotes the number of top data used in the estimation, depending on the degree of censoring.

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arXiv2017

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

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.

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arXiv2015

A Lynden-Bell integral estimator for extremes of randomly truncated data

This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is less heavy-tailed than the truncating variable, asymptotic normality is proved for bothestimators. The proposed estimator of the extreme value index is an adaptation of the Hill estimator, in thenatural form of a Lynden-Bell integral. Simulations illustrate the quality of the estimators under a variety ofsituations.

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arXiv2015

Moment estimators of the extreme value index for randomly censored data in the Weibull domain of attraction

This paper addresses the problem of estimating the extreme value index in presence of random censoring for distributions in the Weibull domain of attraction. The methodologies introduced in [Worms (2014)], in the heavy-tailed case, are adapted here to the negative extreme value index framework, leading to the definition of weighted versions of the popular moments of relative excesses with arbitrary exponent. This leads to the definition of two families of estimators (with an adaptation of the so called Moment estimator as a particular case), for which the consistency is proved under a first order condition. Illustration of their performance, issued from an extensive simulation study, are provided.

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arXiv2010

Empirical Likelihood based Confidence Regions for first order parameters of a heavy tailed distribution

Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed distribution $F$, i.e. such that the common distribution of the excesses over a high threshold $u_n$ can be approximated by a Generalized Pareto Distribution $G_{γ,σ_n}$ with $γ>0$. This work is devoted to the problem of finding confidence regions for the couple $(γ,σ_n)$ : combining the empirical likelihood methodology with estimation equations (close but not identical to the likelihood equations) introduced by J. Zhang (Australian and New Zealand J. Stat n.49(1), 2007), asymptotically valid confidence regions for $(γ,σ_n)$ are obtained and proved to perform better than Wald-type confidence regions (especially those derived from the asymptotic normality of the maximum likelihood estimators). By profiling out the scale parameter, confidence intervals for the tail index are also derived.

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