References
- Ahmad, M. R. 2017. Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality. Communications in Statistics - Theory and Methods 46 (8):3738–3753. doi:https://doi.org/10.1080/03610926.2015.1073310.
- Bai, Z. D., and J. W. Silverstein. 2006. Spectral analysis of large dimensional random matrices. Beijing: SCIENCE PRESS.
- Bartlett, M. S. 1937. Properties of sufficiency and statistical tests. Proc. R. Soc. Lond. A 160:268–282.
- Box, G. E. P. 1949. A general distribution theory for a class of likelihood criteria. Biometrika 36 (3–4):317–346. doi:https://doi.org/10.1093/biomet/36.3-4.317.
- Cai., T., W. Liu, and Y. Xia. 2013. Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings. Journal of the American Statistical Association 108 (501):265–277. doi:https://doi.org/10.1080/01621459.2012.758041.
- Cai, T., and Z. M. Ma. 2013. Optimal hypothesis testing for high dimensional convariance matrices. Bernoulli 19 (5B):2359–2388. doi:https://doi.org/10.3150/12-BEJ455.
- Chao., M., and R. Glaser. 1978. The exact distribution of Bartlett’s test statistic for homogeneity of variances with unequal sample sizes. Journal of the American Statistical Association 73 (362):422–426. doi:https://doi.org/10.1080/01621459.1978.10481594.
- Chen, S. X., L. X. Zhang, and P. S. Zhang. 2010. Tests for high-dimensional covariance matrices. Journal of the American Statistical Association 105 (490):810–819. doi:https://doi.org/10.1198/jasa.2010.tm09560.
- Colonna, J. G., M. Cristo, M. Salvatierra, and E. F. Nakamura. 2015. An incremental technique for real-time bioacoustic signal segmentation. Expert Systems with Applications 42 (21):7367–7374. doi:https://doi.org/10.1016/j.eswa.2015.05.030.
- Dong, F., Y. He, T. Wang, D. Han, H. Lu, H. Zhao, et al. 2020. Predicting viral exposure response from modeling the changes of co-expression networks using time series gene expression data. BMC Bioinformatics 21(370). doi: https://doi.org/10.1186/s12859-020-03705-0.
- Dykstra, R. L. 1970. Establishing the positive definiteness of the sample covariance matrix. The Annals of Mathematical Statistics 41 (6):2153–2154. doi:https://doi.org/10.1214/aoms/1177696719.
- Friendly, M., and M. Sigal. 2020. Visualizing tests for equality of covariance matrices. The American Statistician 2 (74):144–155. doi:https://doi.org/10.1080/00031305.2018.1497537.
- Golub, G. H., and C. F. Van Loan. 2013. Matrix computations. 4th edition ed. The Johns Hopkins University Press. Johns Hopkins University Press 2715 N. Charles St. Baltimore, MD United States. ISBN:978-0-8018-5414-9
- Gupta, A. K., and D. K. Nagar. 2000. Matrix variate distribution. New York: Chapman and Hall/CRC.
- Higuera, C., K. J. Gardiner, K. J. Cios, and Y. Herault. 2015. Self-organizing feature maps identify proteins critical to learning in a mouse model of down syndrome. PLoS ONE [Web Link] journal.pone.0129126. 10 (6):e0129126. doi:https://doi.org/10.1371/journal.pone.0129126.
- Ishll, A., K. Yata, and M. Aoshima. 2019. Equality tests of high-dimensional covariance matrices under the strongly spiked eigenvalue model. Journal of Statistical Planning and Inference 202:99–111. doi:https://doi.org/10.1016/j.jspi.2019.02.002.
- Jiang, D., T. Jiang, and F. Yang. 2012. Likelihood ratio tests for covariance matrices of high-dimensional normal distributions. Journal of Statistical Planning and Inference 142 (8):2241–2256. doi:https://doi.org/10.1016/j.jspi.2012.02.057.
- Jiang, T., and F. Yang. 2013. Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions. The Annals of Statistics 41 (4):2029–2074. doi:https://doi.org/10.1214/13-AOS1134.
- Ledoit, O., and M. Wolf. 2002. Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. The Annals of Statistics 30 (4):1081–1102. doi:https://doi.org/10.1214/aos/1031689018.
- Li, J. and Chen, S. X. (2012. Two sample tests for high-dimensional covariance matrices. {Ann. Statist.}, (40), 908–940.
- Peng, L. H., S. X. Chen, and W. Zhou. 2016. More powerful for tests sparse high-dimensional covariance matrices. Journal of Mutlyivariate Anal 149:124–143. doi:https://doi.org/10.1016/j.jmva.2016.03.008.
- Qiu, Y., and S. X. Chen. 2012. Test for bandedness of high-dimensional covariance matrices and bandwidthe estimation. The Annals of Statistics 40 (3):1285–1314. doi:https://doi.org/10.1214/12-AOS1002.
- Schott, J. R. A. 2007. Test for the equality of covariance matrices when the dimension is large relative to the sample sizes. Computational Statistics and Data Analysis 51 (12):6535–6542. doi:https://doi.org/10.1016/j.csda.2007.03.004.
- Srivastava, M. S. 2005. Some tests concerning the covariance matrix in high dimensional data. Journal of the Japan Statistical Society 35 (2):251–272. doi:https://doi.org/10.14490/jjss.35.251.
- Srivastava, M. S., and H. Yanagihara. 2010. Testing the equality of several covariance matrices with fewer observations than the dimension. Journal of Multivariate Analysis 101 (6):1319–1329. doi:https://doi.org/10.1016/j.jmva.2009.12.010.
- Tsanas, A., Little MA, Fox Cand Ramig LO. 2014. Objective Automatic Assessment of Rehabilitative Speech Treatment in Parkinson’s Disease. IEEE Transaction on Neural Systems and Rehabilitation Engineering 22(1): 181–90. doi: https://doi.org/10.1109/TNSRE.2013.2293575. PMID: 26271131.
- Zhang, Q. Y., J. Hu, and Z. D. Bai. 2020. Modified Pillai’s trace statistics for two high-dimensional sample covariance matrices. Journal of Statistical Planning and Inference 207:255–275. doi:https://doi.org/10.1016/j.jspi.2020.01.002.
- Zhong, P., R. Li, and S. Shanto. 2019. Homogeneity tests of covariance matrices with high-dimensional longitudinal data. Biometrika 106 (3):619–634. doi:https://doi.org/10.1093/biomet/asz011.