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Asymptotic Inference for Rank Correlations

Marc-Oliver Pohle, Jan-Lukas Wermuth, Christian H. Weiß

arXiv 16 Dec 2025 · Statistics — Methodology

arXiv:2512.14609 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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63
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Hoeffding, Wassily (1948) A Class of Statistics with Asymptotically Normal Distribution0.95616688%
2Dehling, Herold and Vogel, Daniel and Wendler, Martin and Wied, Domi… (2017) Testing for changes in Kendall's tau0.9507486%
3Pohle, Marc-Oliver and Wermuth, Jan-Lukas (2025) Proper Correlation Coefficients for Discrete Random Variables self0.8434375%
4Embrechts, Paul and McNeil, Alexander and Straumann, Daniel (2002) Correlation and dependence in risk management: properties and pitfalls0.84333100%
5Ne slehová, Johanna (2007) On rank correlation measures for non-continuous random variables0.7375440%
6Dehling, Herold (2006) Limit theorems for dependent U-statistics0.7373367%
7Denker, Manfred and Keller, Gerhard (1983) On U-statistics and v. Mises' statistics for weakly dependent processes0.7373367%
8Kendall, Maurice G (1938) A new measure of rank correlation0.73732100%
9Genest, Christian and Nešlehová, Johanna (2007) A primer on copulas for count data0.64422100%
10Lun, David and Fischer, Svenja and Viglione, Alberto and Blöschl, Gü… (2023) Significance testing of rank cross-correlations between autocorrelated time series with short-range dependence0.64422100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Proper Correlation Coefficients for Nominal Random Variables0.82294