1. Nonparametric Copula Density Estimation Methodologies.
- Author
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Provost, Serge B. and Zang, Yishan
- Subjects
- *
PROBABILITY density function , *DENSITY , *DISTRIBUTION (Probability theory) , *POLYNOMIAL approximation , *BIVARIATE analysis - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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