Marčenko-Pastur law for Kendall’s tau
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...
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| Format: | Article |
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Institute of Mathematical Statistics
2018
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| Online Access: | http://hdl.handle.net/1721.1/115158 https://orcid.org/0000-0002-6677-5349 https://orcid.org/0000-0002-0135-7162 |
| _version_ | 1811082976237191168 |
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| author | Bandeira, Afonso S. Lodhia, Asad Iqbal Rigollet, Philippe |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bandeira, Afonso S. Lodhia, Asad Iqbal Rigollet, Philippe |
| author_sort | Bandeira, Afonso S. |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T12:16:16Z |
| format | Article |
| id | mit-1721.1/115158 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:16:16Z |
| publishDate | 2018 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1151582022-10-01T08:51:16Z Marčenko-Pastur law for Kendall’s tau Bandeira, Afonso S. Lodhia, Asad Iqbal Rigollet, Philippe Massachusetts Institute of Technology. Department of Mathematics Lodhia, Asad Iqbal Rigollet, Philippe 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 National Science Foundation (U.S.) (Grant NSF-MS-1307704) National Science Foundation (U.S.) (CAREER DMS-1541099) National Science Foundation (U.S.) (DMS-1541100) United States. Defense Advanced Research Projects Agency (W911NF-16-1-0551) United States. Office of Naval Research (N00014-17-1-2147) NEC Corporation 2018-05-02T14:30:03Z 2018-05-02T14:30:03Z 2017 2018-04-24T17:48:52Z Article http://purl.org/eprint/type/JournalArticle 1083-589X http://hdl.handle.net/1721.1/115158 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 https://orcid.org/0000-0002-6677-5349 https://orcid.org/0000-0002-0135-7162 http://dx.doi.org/10.1214/17-ECP59 Electronic Communications in Probability Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/ application/pdf Institute of Mathematical Statistics Electronic Communications in Probability |
| spellingShingle | Bandeira, Afonso S. Lodhia, Asad Iqbal Rigollet, Philippe Marčenko-Pastur law for Kendall’s tau |
| title | Marčenko-Pastur law for Kendall’s tau |
| title_full | Marčenko-Pastur law for Kendall’s tau |
| title_fullStr | Marčenko-Pastur law for Kendall’s tau |
| title_full_unstemmed | Marčenko-Pastur law for Kendall’s tau |
| title_short | Marčenko-Pastur law for Kendall’s tau |
| title_sort | marcenko pastur law for kendall s tau |
| url | http://hdl.handle.net/1721.1/115158 https://orcid.org/0000-0002-6677-5349 https://orcid.org/0000-0002-0135-7162 |
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