Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation

Karel Hron (), Jitka Machalová () and Alessandra Menafoglio ()
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Karel Hron: Faculty of Science, Palacký University
Jitka Machalová: Faculty of Science, Palacký University
Alessandra Menafoglio: Politecnico di Milano

Statistical Papers, 2023, vol. 64, issue 5, No 8, 1629-1667

Abstract: Abstract A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows representing a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities, and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (e.g., through copulas), and allows the analysis of datasets of bivariate densities, in a Functional Data Analysis perspective. A spline representation for bivariate densities is also proposed, providing a computational cornerstone for the developed theory.

Keywords: Compositional data; Functional data; Tensor product splines; Anthropometric data (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01359-z

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