Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions
Kendall’s tau and conditional Kendall’s tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved by averaging. Under structural assumptions on the underlying...
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De Gruyter
2025-04-01
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| Series: | Dependence Modeling |
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| Online Access: | https://doi.org/10.1515/demo-2025-0012 |
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| author | van der Spek Rutger Derumigny Alexis |
| author_facet | van der Spek Rutger Derumigny Alexis |
| author_sort | van der Spek Rutger |
| collection | DOAJ |
| description | Kendall’s tau and conditional Kendall’s tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved by averaging. Under structural assumptions on the underlying Kendall’s tau and conditional Kendall’s tau matrices, we introduce new estimators that have a significantly reduced computational cost while keeping a similar error level. In the unconditional setting, we assume that, up to reordering, the underlying Kendall’s tau matrix is block structured with constant values in each of the off-diagonal blocks. Consequences on the underlying correlation matrix are then discussed. The estimators take advantage of this block structure by averaging over (part of) the pairwise estimates in each of the off-diagonal blocks. Derived explicit variance expressions show their improved efficiency. In the conditional setting, the conditional Kendall’s tau matrix is assumed to have a block structure, for some value of the conditioning variable. Conditional Kendall’s tau matrix estimators are constructed similarly as in the unconditional case by averaging over (part of) the pairwise conditional Kendall’s tau estimators. We establish their joint asymptotic normality and show that the asymptotic variance is reduced compared to the naive estimators. Then, we perform a simulation study that displays the improved performance of both the unconditional and conditional estimators. Finally, the estimators are used for estimating the value at risk of a large stock portfolio; backtesting illustrates the obtained improvements compared to the previous estimators. |
| format | Article |
| id | doaj-art-2ef95085b55841259e728b3941bb2713 |
| institution | DOAJ |
| issn | 2300-2298 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Dependence Modeling |
| spelling | doaj-art-2ef95085b55841259e728b3941bb27132025-08-20T03:07:58ZengDe GruyterDependence Modeling2300-22982025-04-01131pp. 11510.1515/demo-2025-0012Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptionsvan der Spek Rutger0Derumigny Alexis1Department of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, NetherlandsDepartment of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, NetherlandsKendall’s tau and conditional Kendall’s tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved by averaging. Under structural assumptions on the underlying Kendall’s tau and conditional Kendall’s tau matrices, we introduce new estimators that have a significantly reduced computational cost while keeping a similar error level. In the unconditional setting, we assume that, up to reordering, the underlying Kendall’s tau matrix is block structured with constant values in each of the off-diagonal blocks. Consequences on the underlying correlation matrix are then discussed. The estimators take advantage of this block structure by averaging over (part of) the pairwise estimates in each of the off-diagonal blocks. Derived explicit variance expressions show their improved efficiency. In the conditional setting, the conditional Kendall’s tau matrix is assumed to have a block structure, for some value of the conditioning variable. Conditional Kendall’s tau matrix estimators are constructed similarly as in the unconditional case by averaging over (part of) the pairwise conditional Kendall’s tau estimators. We establish their joint asymptotic normality and show that the asymptotic variance is reduced compared to the naive estimators. Then, we perform a simulation study that displays the improved performance of both the unconditional and conditional estimators. Finally, the estimators are used for estimating the value at risk of a large stock portfolio; backtesting illustrates the obtained improvements compared to the previous estimators.https://doi.org/10.1515/demo-2025-0012kendall’s tau matrixblock structurekernel smoothingconditional dependence measureprimary: 62h20secondary: 62f3062g05 |
| spellingShingle | van der Spek Rutger Derumigny Alexis Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions Dependence Modeling kendall’s tau matrix block structure kernel smoothing conditional dependence measure primary: 62h20 secondary: 62f30 62g05 |
| title | Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions |
| title_full | Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions |
| title_fullStr | Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions |
| title_full_unstemmed | Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions |
| title_short | Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions |
| title_sort | fast estimation of kendall s tau and conditional kendall s tau matrices under structural assumptions |
| topic | kendall’s tau matrix block structure kernel smoothing conditional dependence measure primary: 62h20 secondary: 62f30 62g05 |
| url | https://doi.org/10.1515/demo-2025-0012 |
| work_keys_str_mv | AT vanderspekrutger fastestimationofkendallstauandconditionalkendallstaumatricesunderstructuralassumptions AT derumignyalexis fastestimationofkendallstauandconditionalkendallstaumatricesunderstructuralassumptions |