Nonparametric Copula Density Estimation Methodologies

Serge B. Provost () and Yishan Zang
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Serge B. Provost: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 3K7, Canada
Yishan Zang: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 3K7, Canada

Mathematics, 2024, vol. 12, issue 3, 1-35

Abstract: This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels’ empirical copulas, by making use of Bernstein’s approximating polynomials of appropriately selected orders; by differentiating linearized distribution functions evaluated at optimally spaced grid points; and by implementing the kernel density estimation technique in conjunction with a repositioning of the pseudo-observations and a certain criterion for determining suitable bandwidths. Smoother representations of such density estimates can further be secured by approximating them by means of moment-based bivariate polynomials. The various copula density estimation techniques being advocated herein are successfully applied to an actual dataset as well as a random sample generated from a known distribution.

Keywords: copula density estimation; data modeling; nonparametric methodologies; polynomial approximations; pseudo-observations; Sklar’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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