Censoring estimators of a positive tail index

Gomes, M. Ivette; Oliveira, Orlando

doi:10.1016/j.spl.2003.07.011

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…Indeed,γ H Z,k estimates γ whilep k is shown to be a consistent estimator of p = γ 2 /(γ 1 + γ 2 ). Einmahl et al (2008) enhanced the asymptotic analysis of this estimator and generalized this approach by considering any classical EVI estimatorγ Gomes and Oliveira (2003), Gomes and Neves (2011), and Brahimi et al (2015) for other papers in this spirit.…”

Section: A Review Of Estimators Of γmentioning

confidence: 99%

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Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications

Beirlant

Maribe

Verster

2018

Insurance: Mathematics and Economics

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The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring. We review the available estimators, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. A bootstrap algorithm is proposed to construct confidence intervals. We compare these new proposals with the existing estimators through simulation. We conclude this paper with a detailed study of a long-tailed car insurance portfolio, which typically exhibit heavy censoring.

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Section: A Review Of Estimators Of γmentioning

confidence: 99%

“…pk . See also Gomes and Oliveira (2003), Gomes and Neves (2011), and Brahimi et al (2015) for other papers in this spirit.…”

Section: Indeed γHmentioning

confidence: 99%

Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications

Beirlant

Maribe

Verster

2018

Insurance: Mathematics and Economics

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“…Alves (2001) has introduced a new lower bound and Gomes and Oliveira (2003) respectively Li et al (2010) have introduced powers of original statistics. However, the influence function of Hill estimator is slowly increasing but unbounded, thus, the Hill procedure is not robust.…”

Section: Introductionmentioning

confidence: 99%

Weak properties and robustness of t-Hill estimators

et al. 2016

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We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile.

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“…An appropriate way to model this situation is to introduce a random variable Y (called a censoring random variable) such that the observations consist of pairs (Z i , δ i ), 1 ≤ i ≤ n where Z i = min(X i , Y i ), δ i = 1 {Xi≤Yi} and 1 is the indicator function. Estimation of the EVI with censored data was considered in [3], [4], [11], [15] and [16]. For example, Beirlant et al (2007) [3] proposed to estimate γ by the following modified version of Hill's estimator:…”

Section: Introductionmentioning

confidence: 99%

Bayesian estimation of the tail index of a heavy tailed distribution under random censoring

Ameraoui

Boukhetala

Dupuy

2016

Computational Statistics & Data Analysis

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International audienceBayesian estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior distributions of the tail index and their consistency and asymptotic normality are established. Finite-sample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset

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Censoring estimators of a positive tail index

Cited by 8 publications

References 10 publications

Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications

Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications

Weak properties and robustness of t-Hill estimators

Bayesian estimation of the tail index of a heavy tailed distribution under random censoring

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