Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions

Rutger van der Spek and Derumigny Alexis ()
Additional contact information
Rutger van der Spek: Department of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, Netherlands
Derumigny Alexis: Department of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, Netherlands

Dependence Modeling, 2025, vol. 13, issue 1, 46

Abstract: 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.

Keywords: Kendall’s tau matrix; block structure; kernel smoothing; conditional dependence measure (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/demo-2025-0012 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:13:y:2025:i:1:p:46:n:1001

DOI: 10.1515/demo-2025-0012

Access Statistics for this article

Dependence Modeling is currently edited by Giovanni Puccetti

More articles in Dependence Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().