Marčenko-Pastur law for Kendall’s tau
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Author(s)
Bandeira, Afonso S.
Lodhia, Asad Iqbal
Rigollet, Philippe
Date Issued
2017
Journal
Electronic Communications in Probability
Publisher
Institute of Mathematical Statistics
Citation
Bandeira, Afonso S., et al. “Marčenko-Pastur Law for Kendall’s Tau.” Electronic Communications in Probability, vol. 22, no. 0, 2017. © 2018 The Institute of Mathematical Statistics and the Bernoulli Society
Version
Final published version
Abstract
We prove that Kendall’s Rank correlation matrix converges to the Marčenko Pastur law, under the assumption that observations are i.i.d random vectors X[subscript 1 ]…,X[subscript n] with components that are independent and absolutely continuous with respect to the Lebesgue measure. This is the first result on the empirical spectral distribution of a multivariate U-statistic. Keywords: statistics; random matrix theory
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.1214/17-ECP59
