IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v204y2024ics0047259x2400068x.html
   My bibliography  Save this article

Invariant correlation under marginal transforms

Author

Listed:
  • Koike, Takaaki
  • Lin, Liyuan
  • Wang, Ruodu

Abstract

A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent samples. In this paper, we study this invariance property on the Pearson correlation coefficient and its applications. A multivariate random vector is said to have an invariant correlation if its pairwise correlation coefficients remain unchanged under any common marginal transforms. For a bivariate case, we characterize all models of such a random vector via a certain combination of comonotonicity—the strongest form of positive dependence—and independence. In particular, we show that the class of exchangeable copulas with invariant correlation is precisely described by what we call positive Fréchet copulas. In the general multivariate case, we characterize the set of all invariant correlation matrices via the clique partition polytope. We also propose a positive regression dependent model that admits any prescribed invariant correlation matrix. Finally, we show that all our characterization results of invariant correlation, except one special case, remain the same if the common marginal transforms are confined to the set of increasing ones.

Suggested Citation

  • Koike, Takaaki & Lin, Liyuan & Wang, Ruodu, 2024. "Invariant correlation under marginal transforms," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:jmvana:v:204:y:2024:i:c:s0047259x2400068x
    DOI: 10.1016/j.jmva.2024.105361
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2400068X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2024.105361?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McNeil, Alexander J. & Nešlehová, Johanna G. & Smith, Andrew D., 2022. "On attainability of Kendall’s tau matrices and concordance signatures," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Yang, Jingping & Qi, Yongcheng & Wang, Ruodu, 2009. "A class of multivariate copulas with bivariate Frechet marginal copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 139-147, August.
    3. Wang, Bin & Wang, Ruodu & Wang, Yuming, 2019. "Compatible matrices of Spearman’s rank correlation," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 67-72.
    4. Krause, Daniel & Scherer, Matthias & Schwinn, Jonas & Werner, Ralf, 2018. "Membership testing for Bernoulli and tail-dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 240-260.
    5. Yang, Jingping & Cheng, Shihong & Zhang, Lihong, 2006. "Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 267-284, October.
    6. Hofert, Marius & Koike, Takaaki, 2019. "Compatibility And Attainability Of Matrices Of Correlation-Based Measures Of Concordance," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 885-918, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. McNeil, Alexander J. & Nešlehová, Johanna G. & Smith, Andrew D., 2022. "On attainability of Kendall’s tau matrices and concordance signatures," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Janusz Milek, 2020. "Quantum Implementation of Risk Analysis-relevant Copulas," Papers 2002.07389, arXiv.org, revised Mar 2020.
    3. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    4. Hirbod Assa & Liyuan Lin & Ruodu Wang, 2022. "Calibrating distribution models from PELVE," Papers 2204.08882, arXiv.org, revised Jun 2023.
    5. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    6. Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.
    7. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586, arXiv.org, revised Mar 2016.
    8. Yang, Jingping & Qi, Yongcheng & Wang, Ruodu, 2009. "A class of multivariate copulas with bivariate Frechet marginal copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 139-147, August.
    9. Shogo Kato & Toshinao Yoshiba & Shinto Eguchi, 2022. "Copula-based measures of asymmetry between the lower and upper tail probabilities," Statistical Papers, Springer, vol. 63(6), pages 1907-1929, December.
    10. Zheng, Yanting & Luan, Xin & Lu, Xin & Liu, Jiaming, 2023. "A new view of risk contagion by decomposition of dependence structure: Empirical analysis of Sino-US stock markets," International Review of Financial Analysis, Elsevier, vol. 90(C).
    11. Shyamalkumar, Nariankadu D. & Tao, Siyang, 2022. "t-copula from the viewpoint of tail dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    12. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    13. Xu, Hang & Zhang, Juntao & Cheng, Chuntian & Cao, Hui & Lu, Jia & Zhang, Zheng, 2024. "A novel metric for evaluating hydro-wind-solar energy complementarity," Applied Energy, Elsevier, vol. 373(C).
    14. Romera, Rosario & Molanes, Elisa M., 2008. "Copulas in finance and insurance," DES - Working Papers. Statistics and Econometrics. WS ws086321, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Carole Bernard & Jinghui Chen & Steven Vanduffel, 2024. "Modeling coskewness with zero correlation and correlation with zero coskewness," Papers 2412.13362, arXiv.org.
    16. Marek Vochozka & Svatopluk Janek & Zuzana Rowland, 2023. "Coffee as an Identifier of Inflation in Selected US Agglomerations," Forecasting, MDPI, vol. 5(1), pages 1-17, January.
    17. Sourabh Balgi & Jose M. Pe~na & Adel Daoud, 2022. "$\rho$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows," Papers 2209.07111, arXiv.org, revised Aug 2024.
    18. Genest, Christian & Hron, Karel & Nešlehová, Johanna G., 2023. "Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:204:y:2024:i:c:s0047259x2400068x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.