Contributions to the diagonal expansion of a bivariate copula with continuous extensions

Carles M. Cuadras

Journal of Multivariate Analysis, 2015, vol. 139, issue C, 28-44

Abstract: We find some properties and eigendecompositions of two integral operators related to copulas. By using an inner product between two functions via an extension of the covariance, we study the countable set of eigenpairs, which is related to the set of canonical correlations and functions. Then a canonical analysis on the so-called Cuadras–Augé family of copulas is performed, showing the continuous dimensionality of this distribution. A diagonal expansion in terms of an integral is obtained. As a consequence, this continuous expansion allows us to generate a wide family of copulas.

Keywords: Eigenanalysis on integral operators; Symmetric copulas; Diagonal expansions; Mercer’s theorem; Uncountable dimensionality; Continuous canonical correlations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.jmva.2015.02.015

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