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Article: On the sphericity test with large-dimensional observations
Title | On the sphericity test with large-dimensional observations |
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Authors | |
Keywords | Large-dimensional data Large-dimensional sample covariance matrix Sphericity Likelihood ratio test John’s test Nagao’s test CLT for linear spectral statistics Spiked population model |
Issue Date | 2013 |
Publisher | Institute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/ejs |
Citation | Electronic Journal of Statistics, 2013, v. 7, p. 2164-2192 How to Cite? |
Abstract | In this paper, we propose corrections to the likelihood ratio test and John’s test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative. |
Persistent Identifier | http://hdl.handle.net/10722/189449 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 1.256 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Wang, Q | en_US |
dc.contributor.author | Yao, J | en_US |
dc.date.accessioned | 2013-09-17T14:41:47Z | - |
dc.date.available | 2013-09-17T14:41:47Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Electronic Journal of Statistics, 2013, v. 7, p. 2164-2192 | en_US |
dc.identifier.issn | 1935-7524 | - |
dc.identifier.uri | http://hdl.handle.net/10722/189449 | - |
dc.description.abstract | In this paper, we propose corrections to the likelihood ratio test and John’s test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative. | - |
dc.language | eng | en_US |
dc.publisher | Institute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/ejs | - |
dc.relation.ispartof | Electronic Journal of Statistics | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Large-dimensional data | - |
dc.subject | Large-dimensional sample covariance matrix | - |
dc.subject | Sphericity | - |
dc.subject | Likelihood ratio test | - |
dc.subject | John’s test | - |
dc.subject | Nagao’s test | - |
dc.subject | CLT for linear spectral statistics | - |
dc.subject | Spiked population model | - |
dc.title | On the sphericity test with large-dimensional observations | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yao, J: jeffyao@hku.hk | en_US |
dc.identifier.authority | Yao, JJ=rp01473 | en_US |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1214/13-EJS842 | - |
dc.identifier.scopus | eid_2-s2.0-84884942640 | - |
dc.identifier.hkuros | 221517 | en_US |
dc.identifier.volume | 7 | - |
dc.identifier.spage | 2164 | - |
dc.identifier.epage | 2192 | - |
dc.identifier.isi | WOS:000324090100001 | - |
dc.publisher.place | United States | - |
dc.customcontrol.immutable | csl 140409 | - |
dc.identifier.issnl | 1935-7524 | - |