Coskewness under dependence uncertainty.

Carole Bernard; Jinghui Chen; Ludger Rüschendorf; Steven Vanduffel

doi:10.1016/j.spl.2023.109853

Coskewness under dependence uncertainty.

Carole Bernard, Jinghui Chen, Ludger Rüschendorf, Steven Vanduffel

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Abstract

We study the impact of dependence uncertainty on E(X1X2···Xd), Xi∼F_i. Under some conditions on the F_i, explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary F_i. We introduce a notion of “standardized rank coskewness”, which is invariant under strictly increasing transformations and takes values in [-1, 1].

Original language	English
Article number	109853
Number of pages	8
Journal	Statistics & Probability Letters
Volume	199
DOIs	https://doi.org/10.1016/j.spl.2023.109853 https://doi.org/10.1016/j.spl.2023.109853
Publication status	Published - 5 May 2023

Bibliographical note

Funding Information:
The authors thank two reviewers for their valuable hints and remarks which helped to improve the paper. The authors gratefully acknowledge funding from Fonds Wetenschappelijk Onderzoek, Belgium (grants G015320N and S006721N ). Jinghui Chen would like to thank Xin Liu for his comments on the paper.

Publisher Copyright:
© 2023 Elsevier B.V.

Copyright:
Copyright 2023 Elsevier B.V., All rights reserved.

Keywords

Expected product
Higher-order moments
Copula
Coskewness
Risk bounds

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https://www.researchgate.net/publication/369655367_Coskewness_under_dependence_uncertainty

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title = "Coskewness under dependence uncertainty.",

abstract = "We study the impact of dependence uncertainty on E(X1X2···Xd), Xi∼Fi. Under some conditions on the Fi, explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary Fi. We introduce a notion of “standardized rank coskewness”, which is invariant under strictly increasing transformations and takes values in [-1, 1].",

keywords = "Expected product, Higher-order moments, Copula, Coskewness, Risk bounds",

author = "Carole Bernard and Jinghui Chen and Ludger R{\"u}schendorf and Steven Vanduffel",

note = "Funding Information: The authors thank two reviewers for their valuable hints and remarks which helped to improve the paper. The authors gratefully acknowledge funding from Fonds Wetenschappelijk Onderzoek, Belgium (grants G015320N and S006721N ). Jinghui Chen would like to thank Xin Liu for his comments on the paper. Publisher Copyright: {\textcopyright} 2023 Elsevier B.V. Copyright: Copyright 2023 Elsevier B.V., All rights reserved.",

year = "2023",

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doi = "10.1016/j.spl.2023.109853",

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T1 - Coskewness under dependence uncertainty.

AU - Bernard, Carole

AU - Chen, Jinghui

AU - Rüschendorf, Ludger

AU - Vanduffel, Steven

N1 - Funding Information: The authors thank two reviewers for their valuable hints and remarks which helped to improve the paper. The authors gratefully acknowledge funding from Fonds Wetenschappelijk Onderzoek, Belgium (grants G015320N and S006721N ). Jinghui Chen would like to thank Xin Liu for his comments on the paper. Publisher Copyright: © 2023 Elsevier B.V. Copyright: Copyright 2023 Elsevier B.V., All rights reserved.

PY - 2023/5/5

Y1 - 2023/5/5

N2 - We study the impact of dependence uncertainty on E(X1X2···Xd), Xi∼Fi. Under some conditions on the Fi, explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary Fi. We introduce a notion of “standardized rank coskewness”, which is invariant under strictly increasing transformations and takes values in [-1, 1].

AB - We study the impact of dependence uncertainty on E(X1X2···Xd), Xi∼Fi. Under some conditions on the Fi, explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary Fi. We introduce a notion of “standardized rank coskewness”, which is invariant under strictly increasing transformations and takes values in [-1, 1].

KW - Expected product

KW - Higher-order moments

KW - Copula

KW - Coskewness

KW - Risk bounds

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U2 - 10.1016/j.spl.2023.109853

DO - 10.1016/j.spl.2023.109853

M3 - Letter

SN - 0167-7152

VL - 199

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

M1 - 109853

ER -

Coskewness under dependence uncertainty.

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Keywords

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