Nonparametric Copula Density Estimation Methodologies
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/3/398 |
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| author | Serge B. Provost Yishan Zang |
| author_facet | Serge B. Provost Yishan Zang |
| author_sort | Serge B. Provost |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T03:53:03Z |
| format | Article |
| id | doaj.art-c85ebd6fef4946bf925a5de9ff700df5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:53:03Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c85ebd6fef4946bf925a5de9ff700df52024-02-09T15:18:12ZengMDPI AGMathematics2227-73902024-01-0112339810.3390/math12030398Nonparametric Copula Density Estimation MethodologiesSerge B. Provost0Yishan Zang1Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 3K7, CanadaDepartment of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 3K7, CanadaThis 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.https://www.mdpi.com/2227-7390/12/3/398copula density estimationdata modelingnonparametric methodologiespolynomial approximationspseudo-observationsSklar’s theorem |
| spellingShingle | Serge B. Provost Yishan Zang Nonparametric Copula Density Estimation Methodologies Mathematics copula density estimation data modeling nonparametric methodologies polynomial approximations pseudo-observations Sklar’s theorem |
| title | Nonparametric Copula Density Estimation Methodologies |
| title_full | Nonparametric Copula Density Estimation Methodologies |
| title_fullStr | Nonparametric Copula Density Estimation Methodologies |
| title_full_unstemmed | Nonparametric Copula Density Estimation Methodologies |
| title_short | Nonparametric Copula Density Estimation Methodologies |
| title_sort | nonparametric copula density estimation methodologies |
| topic | copula density estimation data modeling nonparametric methodologies polynomial approximations pseudo-observations Sklar’s theorem |
| url | https://www.mdpi.com/2227-7390/12/3/398 |
| work_keys_str_mv | AT sergebprovost nonparametriccopuladensityestimationmethodologies AT yishanzang nonparametriccopuladensityestimationmethodologies |