IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v198y2023ics0047259x2300074x.html
   My bibliography  Save this article

Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation

Author

Listed:
  • Genest, Christian
  • Hron, Karel
  • Nešlehová, Johanna G.

Abstract

Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to construct an orthogonal decomposition of a bivariate probability density into an independence and an interaction part. In this paper, new insights into these results are given by reformulating them using Hilbert space theory, and a multivariate extension is developed using a distributional analog of the Hoeffding–Sobol identity. A connection is also made between the resulting decomposition of a multivariate density and its copula-based representation.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x2300074x
    DOI: 10.1016/j.jmva.2023.105228
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2300074X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105228?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. Seo, Won-Ki & Beare, Brendan K., 2019. "Cointegrated linear processes in Bayes Hilbert space," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 90-95.
    2. 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).
    3. Talská, R. & Menafoglio, A. & Machalová, J. & Hron, K. & Fišerová, E., 2018. "Compositional regression with functional response," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 66-85.
    4. Cambanis, Stamatis, 1977. "Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 551-559, December.
    5. Kamila Fačevicová & Peter Filzmoser & Karel Hron, 2023. "Compositional cubes: a new concept for multi-factorial compositions," Statistical Papers, Springer, vol. 64(3), pages 955-985, June.
    6. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.
    7. Hron, K. & Menafoglio, A. & Templ, M. & Hrůzová, K. & Filzmoser, P., 2016. "Simplicial principal component analysis for density functions in Bayes spaces," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 330-350.
    8. Petersen, Alexander & Zhang, Chao & Kokoszka, Piotr, 2022. "Modeling Probability Density Functions as Data Objects," Econometrics and Statistics, Elsevier, vol. 21(C), pages 159-178.
    9. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.
    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. Petersen, Alexander & Zhang, Chao & Kokoszka, Piotr, 2022. "Modeling Probability Density Functions as Data Objects," Econometrics and Statistics, Elsevier, vol. 21(C), pages 159-178.
    2. Tadao Hoshino, 2024. "Functional Spatial Autoregressive Models," Papers 2402.14763, arXiv.org, revised Oct 2024.
    3. Karel Hron & Jitka Machalová & Alessandra Menafoglio, 2023. "Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation," Statistical Papers, Springer, vol. 64(5), pages 1629-1667, October.
    4. Jitka Machalová & Renáta Talská & Karel Hron & Aleš Gába, 2021. "Compositional splines for representation of density functions," Computational Statistics, Springer, vol. 36(2), pages 1031-1064, June.
    5. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    6. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    7. ARATA Yoshiyuki, 2017. "A Functional Linear Regression Model in the Space of Probability Density Functions," Discussion papers 17015, Research Institute of Economy, Trade and Industry (RIETI).
    8. Seo, Won-Ki & Beare, Brendan K., 2019. "Cointegrated linear processes in Bayes Hilbert space," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 90-95.
    9. Kokoszka, Piotr & Miao, Hong & Petersen, Alexander & Shang, Han Lin, 2019. "Forecasting of density functions with an application to cross-sectional and intraday returns," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1304-1317.
    10. Talská, R. & Menafoglio, A. & Machalová, J. & Hron, K. & Fišerová, E., 2018. "Compositional regression with functional response," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 66-85.
    11. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    12. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    13. Zhu, Changbo & Müller, Hans-Georg, 2024. "Spherical autoregressive models, with application to distributional and compositional time series," Journal of Econometrics, Elsevier, vol. 239(2).
    14. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    15. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    16. Pawlak, Jacek & Polak, John W. & Sivakumar, Aruna, 2017. "A framework for joint modelling of activity choice, duration, and productivity while travelling," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 153-172.
    17. H'el`ene Cossette & Etienne Marceau & Alessandro Mutti & Patrizia Semeraro, 2024. "Generalized FGM dependence: Geometrical representation and convex bounds on sums," Papers 2406.10648, arXiv.org, revised Oct 2024.
    18. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    19. Mario Jovanovic, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers 0240, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    20. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.

    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:198:y:2023:i:c:s0047259x2300074x. 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.