Semi-parametric second-order reduced-bias high quantile estimation

Caeiro, Frederico; Gomes, M. Ivette

doi:10.1007/s11749-008-0108-8

Cited by 15 publications

(10 citation statements)

References 21 publications

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“…Gomes and Pestana have used the RB EVI‐estimators in to build corrected Weissman‐Hill estimators, denoted by

Q_{p, {\overset{ξ}{true}}_{n}^{C H}} false(k false)

. For heavy right‐tails, related works also dealt with RB extreme quantile estimation, one of the topics under consideration in this article. These classes of RB extreme quantile estimators are also less sensitive to the choice of k when compared to the classic Weissman‐Hill estimators.…”

Section: Estimation Of the Extreme Value Parametersmentioning

confidence: 99%

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A simple class of reduced bias kernel estimators of extreme value parameters

Caeiro

Henriques‐Rodrigues

Gomes

2019

Comp and Math Methods

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In Statistics of Extremes, we often have to deal with the estimation of the extreme value index, a key parameter of extreme events. The adequate estimation of this parameter is of crucial importance in the estimation of other parameters of extreme events, such as an extreme quantile, a small exceedance probability, or the return period of a high level. In this paper, we first analyze a class of kernel estimators that generalize the classical Hill estimator of the extreme value index. Then, to improve the accuracy of the estimation, we also propose a new class of reduced bias kernel estimators, parameterized with a tuning parameter that allow us to change the asymptotic mean squared error. Under suitable conditions, such class of estimators is consistent and has asymptotic normal distribution with a null dominant component of asymptotic bias. As a result, we show that further bias reduction is possible with an adequate choice of the tuning parameter. Additionally, semiparametric reduced‐bias extreme quantiles estimators based on kernel estimators of the extreme value index are also put forward. Under adequate conditions on the underlying model, we establish the consistency and asymptotic normality of these extreme quantile estimators. Finally, we analyze the log‐returns of the BOVESPA stock market index, collected from 2004 to 2016.

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“…Gomes and Pestana have used the RB EVI‐estimators in to build corrected Weissman‐Hill estimators, denoted by

Q_{p, {\overset{ξ}{true}}_{n}^{C H}} false(k false)

Section: Estimation Of the Extreme Value Parametersmentioning

confidence: 99%

“…Using the same type of arguments as in (27), and under the same conditions, ie, for intermediate k such that √ kA(n∕k) → 1 , finite, with r n satisfying (28), we can also state the asymptotic behavior of the extreme quantile estimator in (12), ie,…”

Section: Asymptotic Behavior Of the Extreme Quantile Estimators Undermentioning

confidence: 99%

A simple class of reduced bias kernel estimators of extreme value parameters

Caeiro

Henriques‐Rodrigues

Gomes

2019

Comp and Math Methods

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“…Gomes & Pestana and Beirlant et al , incorporate the MVRB EVI estimators in Caeiro et al , and Gomes et al , in high‐quantile semi‐parametric estimation. See also Diebolt et al , , Beirlant et al , , Caeiro & Gomes and Li et al , . For a SORB estimation of the Weibull‐tail coefficient, we mention Diebolt et al , .…”

Section: Semi‐parametric Estimation Of Other Parametersmentioning

confidence: 99%

Extreme Value Theory and Statistics of Univariate Extremes: A Review

Gomes

Guillou

2014

Int Statistical Rev

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148

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International audienceStatistical issues arising in modelling univariate extremes of a random sample have been successfully used in the most diverse fields, such as biometrics, finance, insurance and risk theory. Statistics of univariate extremes (SUE), the subject to be dealt with in this review paper, has recently faced a huge development, partially because rare events can have catastrophic consequences for human activities, through their impact on the natural and constructed environments. In the last decades, there has been a shift from the area of parametric SUE, based on probabilistic asymptotic results in extreme value theory, towards semi-parametric approaches. After a brief reference to Gumbel's block methodology and more recent improvements in the parametric framework, we present an overview of the developments on the estimation of parameters of extreme events and on the testing of extreme value conditions under a semi-parametric framework. We further discuss a few challenging topics in the area of SUE. univariate extremes; parametric and semi-parametric approaches; extreme value index and tail parameters; testing issues

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“…I: Your interest in the parametric approach to statistical inference in extreme values [10,18,19,21,25] has gradually shifted to an approach typically classified as semiparametric [2,11,29,33], sometimes combined with resampling methods [30,31]. Can these approaches be viewed as complementary?…”

Section: Imentioning

confidence: 99%

An interview with Ivette Gomes

Alves

Carvalho

2015

Extremes

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Maria Ivette Gomes was born July 21, 1948 in Almada, Portugal. After obtaining a BSc in Pure Mathematics in 1970 from the University of Lisbon, Ivette moved in to the University of Sheffield where she completed her PhD in Statistics in 1978, under the supervision of Clive Anderson. Research on statistics of extremes in Portugal has now a long tradition, with Ivette being one of the founders of the movement, along with Tiago de Oliveira (1928-1992). Ivette was co-founder of the Portuguese Statistical Society, and acted as its President from 1990 until 1994; since 1975 she played a key role in the Center of Statistics and Applications (CEAUL), being its scientific coordinator from 1999 until 2006. She was Professor at the Department of Statistics and Operations Research, University of Lisbon, from 1986 until her retirement in 2011. She has been an influential and distinguished scientist in the field of statistics of extremes, through her research, teaching and supervision activities, as well an ambassador of the 'school of extremes' in Portugal.

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Semi-parametric second-order reduced-bias high quantile estimation

Abstract: Heavy tails, High quantiles, Semi-parametric estimation, Statistics of extremes, 62G32, 62E20, 65C05,

Cited by 15 publications

References 21 publications

A simple class of reduced bias kernel estimators of extreme value parameters

A simple class of reduced bias kernel estimators of extreme value parameters

Extreme Value Theory and Statistics of Univariate Extremes: A Review

An interview with Ivette Gomes

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