Kernel regression with Weibull-type tails

Wet, Tertius de; Goegebeur, Yuri; Guillou, Armelle; Osmann, Michael

doi:10.1007/s10463-015-0531-z

Cited by 8 publications

(11 citation statements)

References 29 publications

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“…Next, we provide some information regarding the distributional behavior of V ik , defined in (7). Suppose that Y 1:n ,…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…The class of models with a Weibull-type tail is quite broad and includes, among others, the normal, the gamma, the Weibull, and the logistic distributions. This type of models is quite useful in several areas of applications such as hydrology, meteorology, environmental sciences, and nonlife insurance (see de Wet et al [7]). Further note that condition (4) is equivalent to assume that the inverse cumulative hazard function H ⟵ is a regularly varying function with index θ. Thus,…”

Section: Introductionmentioning

confidence: 99%

“…with V ik defined in (7). Consistency of the Hill estimator for ξ holds if k = kðnÞ is an intermediate sequence, i.e., if…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient

Caeiro

Henriques‐Rodrigues

Gomes

2022

Computational and Mathematical Methods

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Due to the specificity of the Weibull tail coefficient, most of the estimators available in the literature are based on the log excesses and are consequently quite similar to the estimators used for the estimation of a positive extreme value index. The interesting performance of estimators based on generalized means leads us to base the estimation of the Weibull tail coefficient on the power mean-of-order- p . Consistency and asymptotic normality of the estimators under study are put forward. Their performance for finite samples is illustrated through a Monte Carlo simulation. It is always possible to find a negative value of p (contrarily to what happens with the mean-of-order- p estimator for the extreme value index), such that, for adequate values of the threshold, there is a reduction in both bias and root mean square error.

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“…Next, we provide some information regarding the distributional behavior of V ik , defined in (7). Suppose that Y 1:n ,…”

Section: Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient

Caeiro

Henriques‐Rodrigues

Gomes

2022

Computational and Mathematical Methods

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“…In fact, Gardes & Girard (2016) estimated the conditional tail coefficient of Weibull-type distributions when functional covariate is available. de Wet et al (2016) considered the estimation of the tail coefficient of a Weibull-type distribution in the presence of real random covariates. Worms & Worms (2019) proposed an estimator of the Weibull-tail coefficient when the Weibull-tail distribution of interest is censored from the right by another Weibull-tail distribution.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric kernel estimation of Weibull-tail coefficient in presence of the right random censoring

Ushize¹,

Diop²

2021

Preprint

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In this paper, nonparametric estimation of the conditional Weibull-tail coefficient when the variable of interest is right random censored is addressed. A Weissman-type estimator of conditional extreme quantile is also proposed. In addition, a simulation study is conducted to assess the finite-sample behavior of the proposed estimators and a comparison with alternative strategies is provided. Finally, the practical applicability of the methodology is presented using a real datasets of men suffering from a larynx cancer.

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“…In contrast, there are only few studies on investigating the extremal behavior of Weibull-type tails under the regression setting. Among limited literature, de Wet et al (2016) con-sidered the estimation of the tail coefficient of a Weibull-type distribution and of the extreme conditional quantiles based on kernel statistics. Gardes and Girard (2016) focused only on the estimation of the tail-coefficient of a Weibull-type distribution based on a kernel estimator of extreme conditional quantiles.…”

Section: Introductionmentioning

confidence: 99%

Extremal linear quantile regression with Weibull-type tails

Wang

Tong³

2020

STAT SINICA

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This paper studies the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. The work fills a gap in the literature of extreme quantile regression where many important Weibull-type distributions are excluded by the assumed strong conditions. We demonstrate through simulation study that the proposed Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) Extremal linear quantile regression with Weibull-type tails extrapolation method provides more efficient and stable estimation of conditional quantiles of extreme orders than the conventional method.The practical value of the proposed method is demonstrated through the analysis of extremely high birth weight.

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Kernel regression with Weibull-type tails

Cited by 8 publications

References 29 publications

The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient

The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient

Nonparametric kernel estimation of Weibull-tail coefficient in presence of the right random censoring

Extremal linear quantile regression with Weibull-type tails

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