Fitting Copulas with Maximal Entropy
We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). Th...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/1/87 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588523443585024 |
|---|---|
| author | Milan Bubák Mirko Navara |
| author_facet | Milan Bubák Mirko Navara |
| author_sort | Milan Bubák |
| collection | DOAJ |
| description | We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions. |
| format | Article |
| id | doaj-art-f2c0afda66b4435bb225919e03bf8dfe |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-f2c0afda66b4435bb225919e03bf8dfe2025-01-24T13:31:57ZengMDPI AGEntropy1099-43002025-01-012718710.3390/e27010087Fitting Copulas with Maximal EntropyMilan Bubák0Mirko Navara1Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, CZ-166 27 Prague, Czech RepublicDepartment of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, CZ-166 27 Prague, Czech RepublicWe deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.https://www.mdpi.com/1099-4300/27/1/87maximum entropy estimatorcopuladensityconvex optimization |
| spellingShingle | Milan Bubák Mirko Navara Fitting Copulas with Maximal Entropy Entropy maximum entropy estimator copula density convex optimization |
| title | Fitting Copulas with Maximal Entropy |
| title_full | Fitting Copulas with Maximal Entropy |
| title_fullStr | Fitting Copulas with Maximal Entropy |
| title_full_unstemmed | Fitting Copulas with Maximal Entropy |
| title_short | Fitting Copulas with Maximal Entropy |
| title_sort | fitting copulas with maximal entropy |
| topic | maximum entropy estimator copula density convex optimization |
| url | https://www.mdpi.com/1099-4300/27/1/87 |
| work_keys_str_mv | AT milanbubak fittingcopulaswithmaximalentropy AT mirkonavara fittingcopulaswithmaximalentropy |