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

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  • 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
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    References listed on IDEAS

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