A Jarque-Bera test for sphericity of a large-dimensional covariance matrix
AbstractThis article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X ∼ Nd(µ,Σ). This test is applicable if the sample size, n + 1, and d both go to infinity while d/n → y ∈ (0,∞), provided that the limits of tr(Σk)/d, k = 1,...,8, are finite. The main idea of this test is to check whether the empirical eigenvalue distribution of a suitably standardized sample covariance matrix obeys the semicircle law. Due to similarities of the semicircle law to the normal distribution, the proposed test statistic is of the type of the Jarque-Bera test statistic. Simulation results show that the new sphericity test outperforms the tests from the current literature for certain local alternatives if y is small. --
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 1/13.
Date of creation: 2013
Date of revision:
Contact details of provider:
Postal: Albertus Magnus Platz, 50923 Köln
Phone: 0221 / 470 5607
Fax: 0221 / 470 5179
Web page: http://www.wisostat.uni-koeln.de/Englisch/index_en.html
More information through EDIRC
Test for covariance matrix; High-dimensional data; Spectral distribution; Semicircle law; Free cumulant; Jarque-Bera test;
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
- Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
- Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
- Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics).
If references are entirely missing, you can add them using this form.