Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 93, 2021 - Issue 3
118
Views
0
CrossRef citations to date
0
Altmetric
Articles

High-dimensional Edgeworth expansion of the determinant of sample correlation matrix and its error bound

&
Pages 428-446 | Received 07 Mar 2019, Accepted 16 Mar 2020, Published online: 27 Mar 2020

References

  • T. Akita, J. Jin, and H. Wakaki, High-dimensional Edgeworth expansion of a test statistic on independence and its error bound, J. Multivariate Anal. 101(8) (2010), pp. 1806–1813. doi: 10.1016/j.jmva.2010.03.014
  • M.S. Bartlett, A note on multiplying factors for various chi-squared approximations, J. R. Stat. Soc. Ser. B. 16 (1954), pp. 296–298.
  • C.G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math. 77 (1945), pp. 1–125. doi: 10.1007/BF02392223
  • Y. Fujikoshi, Error bounds for asymptotic approximations of the linear discriminant function when the sample size and dimensionality are large, J. Multivariate Anal. 73 (2000), pp. 1–17. doi: 10.1006/jmva.1999.1862
  • Y. Fujikoshi, V.V. Ulyanov, and R. Shimizu, Multivariate Statistics: High Dimensional and Large Sample Approximations, John Wiley & Sons Inc., New York, 2010.
  • A.K. Gupta and D.K. Nagar, Distribution of the determinant of the sample correlation matrix from a mixture normal model, Random Oper. Stoch. Equ. 12(2) (2004), pp. 193–199. doi: 10.1515/156939704323074728
  • T. Jiang, Determinant of sample correlation matrix with application, Ann. Appl. Probab. 29(3) (2019), pp. 1356–1397. doi: 10.1214/17-AAP1362
  • T. Jiang and Y. Qi, Likelihood ratio tests for high-dimensional normal distributions, Scand. J. Stat.42(4) (2015), pp. 988–1009. doi: 10.1111/sjos.12147
  • T. Jiang and F. Yang, Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions, Ann. Statist. 41(4) (2013), pp. 2029–2074. doi: 10.1214/13-AOS1134
  • N. Kato, T. Yamada, and Y. Fujikoshi, High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound, J. Multivariate Anal. 101 (2010), pp. 101–112. doi: 10.1016/j.jmva.2009.05.006
  • M. Mitsui, K. Koizumi, and T. Seo, Likelihood ratio test statistic for block compound symmetry covariance structure and its asymptotic expansion, Technical Report No.15-03, Statistical Research Group, Hiroshima University, Japan, 2015.
  • R.J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons Inc., New York, 1982.
  • V.V. Ulyanov, H. Wakaki, and Y. Fujikoshi, Berry-Esseen bound for high-dimensional asymptotic approximation of Wilk's lambda distribution, Statist. Probab. Lett. 76 (2006), pp. 1191–1200. doi: 10.1016/j.spl.2005.12.027
  • T. Yamada, High-dimensional Edgeworth expansion of LR statistic for testing circular symmetric covariance structure and its error bound, Comm. Statist. Theory Methods 41 (2012), pp. 1887–1910. doi: 10.1080/03610926.2011.552826

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.