Marc-Oliver Pohle, Jan-Lukas Wermuth, Christian H. Weiß
arXiv 16 Dec 2025 · Statistics — Methodology
arXiv:2512.14609 · PDF · DOI · OpenAlex · Extracted main text
Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for classical rank correlations, including Kendall's tau, Spearman's rho, Goodman-Kruskal's gamma, Kendall's tau-b, and grade correlation. We derive asymptotic distributions for both iid and time series data, resorting to asymptotic results for U-statistics, and introduce consistent variance estimators. This enables the construction of confidence intervals and tests, generalizes classical results for continuous random variables and leads to corrected versions of widely used tests of independence. We analyze the finite-sample performance of our variance estimators, confidence intervals, and tests in simulations and illustrate their use in case studies.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hoeffding, Wassily (1948) A Class of Statistics with Asymptotically Normal Distribution | 0.956 | 16 | 6 | 88% |
| 2 | Dehling, Herold and Vogel, Daniel and Wendler, Martin and Wied, Domi… (2017) Testing for changes in Kendall's tau | 0.950 | 7 | 4 | 86% |
| 3 | Pohle, Marc-Oliver and Wermuth, Jan-Lukas (2025) Proper Correlation Coefficients for Discrete Random Variables self | 0.843 | 4 | 3 | 75% |
| 4 | Embrechts, Paul and McNeil, Alexander and Straumann, Daniel (2002) Correlation and dependence in risk management: properties and pitfalls | 0.843 | 3 | 3 | 100% |
| 5 | Ne slehová, Johanna (2007) On rank correlation measures for non-continuous random variables | 0.737 | 5 | 4 | 40% |
| 6 | Dehling, Herold (2006) Limit theorems for dependent U-statistics | 0.737 | 3 | 3 | 67% |
| 7 | Denker, Manfred and Keller, Gerhard (1983) On U-statistics and v. Mises' statistics for weakly dependent processes | 0.737 | 3 | 3 | 67% |
| 8 | Kendall, Maurice G (1938) A new measure of rank correlation | 0.737 | 3 | 2 | 100% |
| 9 | Genest, Christian and Nešlehová, Johanna (2007) A primer on copulas for count data | 0.644 | 2 | 2 | 100% |
| 10 | Lun, David and Fischer, Svenja and Viglione, Alberto and Blöschl, Gü… (2023) Significance testing of rank cross-correlations between autocorrelated time series with short-range dependence | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 63 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Proper Correlation Coefficients for Nominal Random Variables | 0.822 | 9 | 4 |