Distinguishing Log-Concavity from Heavy Tails

Asmussen, Søren; Lehtomaa, Jaakko

doi:10.3390/risks5010010

Cited by 10 publications

(21 citation statements)

References 23 publications

(28 reference statements)

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“…Choosing it orthogonal to the minimizing geodesic between both sets and close to the boundary of the set S, S belongs entirely to one half of S d−1 and B(x, δ/3) ∩ S d−1 to the other half. This choice of the separating hyperplane is possible due to the assumption P(U ∈ S) < 1 2 and the uniform distribution of U. If P(U ∈ S) = 1 2 , one can take instead of a separating hyperplane the supporting hyperplane of S that bisects the unit sphere.…”

Section: Consistency Of Estimatorsmentioning

confidence: 99%

“…This choice of the separating hyperplane is possible due to the assumption P(U ∈ S) < 1 2 and the uniform distribution of U. If P(U ∈ S) = 1 2 , one can take instead of a separating hyperplane the supporting hyperplane of S that bisects the unit sphere.…”

Section: Consistency Of Estimatorsmentioning

confidence: 99%

“…To answer the question on what causes the heavy-tailedness of multivariate data, one usually selects a suitable norm • and analyses the resulting onedimensional distribution of X with standard procedures, such as the mean excess plot [4,8,9] or alternative methods such as the ones in [1]. In practice, given the heaviness identified from the distribution of X , the aim is to analyse the distribution of U and the dependence structure between R and U.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the identification of the riskiest directional components from multivariate heavy-tailed data

Hägele¹,

Lehtomaa²

2021

Preprint

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In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and algorithms for detecting dominating directional components in multivariate data.We study general heavy-tailed multivariate random vectors in dimension d ≥ 2 and present consistent estimators which can be used to evaluate why the data is heavy-tailed. This is done by identifying the set of the riskiest directional components. The results are of particular interest in insurance when setting reinsurance policies and in finance when hedging a portfolio of multiple assets.

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Section: Consistency Of Estimatorsmentioning

confidence: 99%

Section: Consistency Of Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the identification of the riskiest directional components from multivariate heavy-tailed data

Hägele¹,

Lehtomaa²

2021

Preprint

Self Cite

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“…random variables X, X 1 , X 2 , … > 0 with common distribution function F having density f . Asmussen and Lehtomaa (2017) introduced the function g ∶ (0, ∞) → [0, 1], defined by…”

Section: Introductionmentioning

confidence: 99%

A gamma tail statistic and its asymptotics

Iwashita,

Klar

2023

Statistica Neerlandica

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Asmussen and Lehtomaa [Distinguishing log‐concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function g which is able to distinguish between log‐convex and log‐concave tail behaviour of distributions, and proposed a randomized estimator for g. In this paper, we show that g can also be seen as a tool to detect gamma distributions or distributions with gamma tail. We construct a more efficient estimator ĝn based on U‐statistics, propose several estimators of the (asymptotic) variance of ĝn, and study their performance by simulations. Finally, the methods are applied to several data sets of daily precipitation.This article is protected by copyright. All rights reserved.

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“…However, for income data, log-concavity based methods should be used with caution since distributions with log-concave density are always sub-exponential , whereas income data can have heavier tails. Diagnostic tools such as those in Asmussen and Lehtomaa (2017) can be used to enquire if the data has heavier tail, e.g. regular varying tails, in these cases.…”

Section: Introductionmentioning

confidence: 99%

Improved inference for vaccine-induced immune responses via shape-constrained methods

Laha

Moodie

Huang

et al. 2022

Electron. J. Statist.

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We study the performance of shape-constrained methods for evaluating immune response profiles from early-phase vaccine trials. The motivating problem for this work involves quantifying and comparing the IgG binding immune responses to the first and second variable loops (V1V2 region) arising in HVTN 097 and HVTN 100 HIV vaccine trials. We consider unimodal and log-concave shape-constrained methods to compare the immune profiles of the two vaccines, which is reasonable because the data support that the underlying densities of the immune responses could have these shapes. To this end, we develop novel shape-constrained tests of stochastic dominance and shape-constrained plug-in estimators of the squared Hellinger distance between two densities. Our techniques are either tuning parameter free, or rely on only one tuning parameter, but their performance is either better (the tests of stochastic dominance) or comparable with the nonparametric methods (the estimators of the squared Hellinger distance). The minimal dependence on tuning parameters is especially desirable in clinical contexts where analyses must be prespecified and reproducible. Our methods are supported by theoretical results and simulation studies.

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Distinguishing Log-Concavity from Heavy Tails

Cited by 10 publications

References 23 publications

On the identification of the riskiest directional components from multivariate heavy-tailed data

On the identification of the riskiest directional components from multivariate heavy-tailed data

A gamma tail statistic and its asymptotics

Improved inference for vaccine-induced immune responses via shape-constrained methods

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