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

Christian Genest, Karel Hron and Johanna G. Nešlehová

Journal of Multivariate Analysis, 2023, vol. 198, issue C

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.

Keywords: Bayes spaces; Copulas; Dependence structure; Hilbert space; Orthogonal decomposition (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2023.105228

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