Kernel estimation of the tail index of a right-truncated Pareto-type distribution

Benchaira, Souad; Meraghni, Djamel; Necir, Abdelhakim

doi:10.1016/j.spl.2016.08.004

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…In view of the previous weak approximation, the authors also proved that if, given n = m, Benchaira et al (2016b) followed this approach to introduce a kernel estimator to γ 1 which improves the bias of γ (W) 1…”

Section: Introductionmentioning

confidence: 98%

A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

Haouas¹,

Necir²,

Meraghni³

et al. 2017

JAS

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By means of a Lynden-Bell integral with deterministic threshold, Worms and Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab.Lett. 2016; 109: 106-117] recently introduced an asymptotically normal estimator of the tail index for randomly right-truncated Pareto-type data. In this context, we consider the random threshold case to derive a Hill-type estimator and establish its consistency and asymptotic normality. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator.

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Section: Introductionmentioning

confidence: 98%

A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

Haouas¹,

Necir²,

Meraghni³

et al. 2017

JAS

Self Cite

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show abstract

“…By using Potter's inequalities, see e.g. Proposition B.1.10 in de Haan and Ferreira (2006), to the regularly varying function Benchaira et al (2016) showed that…”

Section: 1mentioning

confidence: 99%

“…For an overview of the kernel estimates of the tail index for complete data, one refers to Hüsler et al (2006), Ciuperca and Mercadier (2010), Goregebeur et al (2010) and Caeiro and Henriques-Rodrigues (2019) and references therein. Motivated by the qualities of this estimation method, recently Benchaira et al (2016) proposed a kernel estimator of the tail index for randomly truncated data and established its asymptotic normality. To the best of our knowledge, when the data are randomly censored, this estimation approach is not yet addressed in the extreme value literature.…”

mentioning

confidence: 99%

Kernel estimation for the tail index of a right-censored Pareto-type distribution

Necir,

Soltane

2021

Preprint

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We introduce a kernel estimator, to the tail index of a right-censored Pareto-type distribution, that generalizes Worms's one (Worms and Worms, 2014) in terms of weight coefficients. Under some regularity conditions, the asymptotic normality of the proposed estimator is established. In the framework of the second-order condition, we derive an asymptotically bias-reduced version to the new estimator.Through a simulation study, we conclude that one of the main features of the proposed kernel estimator is its smoothness contrary to Worms's one, which behaves, rather erratically, as a function of the number of largest extreme values. As expected, the bias significantly decreases compared to that of the non-smoothed estimator with however a slight increase in the mean squared error.

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“…with {W (s) ; s ≥ 0} being a standard Wiener process defined on the probability space (Ω, A, P) . Thereby, they conclude that √ k γ Benchaira et al (2016b) adopted the same approach to introduce a kernel estimator to the tail index γ 1 which improves the bias of γ…”

Section: Introductionmentioning

confidence: 99%

Estimating the Second-Order Parameter of Regular Variation and Bias Reduction in Tail Index Estimation Under Random Truncation

Haouas

Necir

Brahimi

2018

J Stat Theory Pract

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In this paper, we propose an estimator of the second-order parameter of randomly righttruncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator of the tail index and study its asymptotic behaviour. Our considerations are based on a useful Gaussian approximation of the tail product-limit process recently given by Benchaira et al. [Tail product-limit process for truncated data with application to extreme value index estimation. Extremes, 2016; 19: 219-251] and the results of Gomes et al. [Semi-parametric estimation of the second order parameter in statistics of extremes. Extremes, 2002; 5: 387-414]. We show, by simulation, that the proposed estimators behave well, in terms of bias and mean square error.

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Kernel estimation of the tail index of a right-truncated Pareto-type distribution

Cited by 7 publications

References 13 publications

A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

Kernel estimation for the tail index of a right-censored Pareto-type distribution

Estimating the Second-Order Parameter of Regular Variation and Bias Reduction in Tail Index Estimation Under Random Truncation

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