Adaptive estimation of a tail shape second order parameter: A computational comparative study

Caeiro, Frederico; Gomes, Dora Prata

doi:10.1063/1.4938771

Cited by 5 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is equivalent to assume that the tail quantile function of the underlying model can be written as

U (t) = c t^{ξ} (1 + ξ β t^{ρ} / ρ + O (t^{2 ρ})), as t \to \infty .

Among the models, used in applications, under slightly restrictive third‐order condition, we mention the Fréchet, the Student t , the Burr, or the generalized Pareto. Algorithms for the estimation of the second‐order parameters ( ρ , β ) can be found in previous studies, among others.…”

Section: Results For the Classes Of Kernel Evi Estimatorsmentioning

confidence: 99%

“…Among the models, used in applications, under slightly restrictive third-order condition, we mention the Fréchet, the Student t, the Burr, or the generalized Pareto. Algorithms for the estimation of the second-order parameters ( , ) can be found in previous studies, [22][23][24] among others.…”

Section: Second-and Third-order Conditions For a Heavy Right Tail Modelmentioning

confidence: 99%

“…It is worth to mention that all RB EVI estimators considered in this section can be third-order reduced bias estimators, ie, can haveb • = 0 in (24) for certain values of the parameters ( , ). For the estimator̃C H n (k), in (20), the asymptotic bias is null if and only if the parameters ( , ) satisfy the relation…”

Section: Asymptotic Behaviour Of the Reduced-bias Estimatorsmentioning

confidence: 99%

See 2 more Smart Citations

Reduced‐bias kernel estimators of a positive extreme value index

Caeiro

Henriques‐Rodrigues

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we deal with the semi‐parametric estimation of the extreme value index, an important parameter in extreme value analysis. It is well known that many classic estimators, such as the Hill estimator, reveal a strong bias. This problem motivated the study of two classes of kernel estimators. Those classes generalize the classical Hill estimator and have a tuning parameter that enables us to modify the asymptotic mean squared error and eventually to improve their efficiency. Since the improvement in efficiency is not very expressive, we also study new reduced bias estimators based on the two classes of kernel statistics. Under suitable conditions, we prove their asymptotic normality. Moreover, an asymptotic comparison, at optimal levels, shows that the new classes of reduced bias estimators are more efficient than other reduced bias estimator from the literature. An illustration of the finite sample behaviour of the kernel reduced‐bias estimators is also provided through the analysis of a data set in the field of insurance.

show abstract

“…This is equivalent to assume that the tail quantile function of the underlying model can be written as

U (t) = c t^{ξ} (1 + ξ β t^{ρ} / ρ + O (t^{2 ρ})), as t \to \infty .

Section: Results For the Classes Of Kernel Evi Estimatorsmentioning

confidence: 99%

Section: Second-and Third-order Conditions For a Heavy Right Tail Modelmentioning

confidence: 99%

Section: Asymptotic Behaviour Of the Reduced-bias Estimatorsmentioning

confidence: 99%

See 1 more Smart Citation

Reduced‐bias kernel estimators of a positive extreme value index

Caeiro

Henriques‐Rodrigues

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Both parameters were chosen via bootstrap methodology. In [55], the adaptive estimation of either k or u through a nonparametric bootstrap methodology was considered. An improved version of Hall's bootstrap methodology was introduced and compared with the double bootstrap methodology.…”

Section: Research Mainly Involving the Bootstrapmentioning

confidence: 99%

The PORTSEA (Portuguese School of Extremes and Applications) and a few personal scientific achievements

Gomes

2024

Communications in Mathematics

View full text Add to dashboard Cite

The Portuguese School of Extremes and Applications is nowadays well recognised by the international scientific community, and in my opinion, the organisation of a NATO Advanced Study Institute on Statistical Extremes and Applications, which took place at Vimeiro in the summer of 1983, was a landmark for the international recognition of the group. The dynamic of publication has been very high and the topics under investigation in the area of Extremes have been quite diverse. In this article, attention will be paid essentially to some of the scientific achievements of the author in this field.

show abstract

“…Consistency and asymptotic normality of the estimators in (15) were proved in. 33 The theoretical and simulated results in, [33][34][35] together with their use in RB estimation, lead us to suggest the use of 𝜏 = 0 for 𝜌 ∈ [−1, 0) and 𝜏 = 1 for 𝜌 ∈ (−∞, −1). Other estimators of the shape second-order parameter 𝜌 can be found in, 29,34,[36][37][38] among others.…”

Section: Second-order Regular Variationmentioning

confidence: 99%

A class of weighted Hill estimators

Caeiro

Mateus

Soltane

2021

Comp and Math Methods

Self Cite

View full text Add to dashboard Cite

In Statistics of Extremes, the estimation of the extreme value index is an essential requirement for further tail inference. In this work, we deal with the estimation of a strictly positive extreme value index from a model with a Pareto-type right tail. Under this framework, we propose a new class of weighted Hill estimators, parameterized with a tuning parameter a. We derive their non-degenerate asymptotic behavior and analyze the influence of the tuning parameter in such result. Their finite sample performance is analyzed through a Monte Carlo simulation study. A comparison with other important extreme value index estimators from the literature is also provided.

show abstract

Adaptive estimation of a tail shape second order parameter: A computational comparative study

Cited by 5 publications

References 18 publications

Reduced‐bias kernel estimators of a positive extreme value index

Reduced‐bias kernel estimators of a positive extreme value index

The PORTSEA (Portuguese School of Extremes and Applications) and a few personal scientific achievements

A class of weighted Hill estimators

Contact Info

Product

Resources

About