References
- Rencher AC. Methods of multivariate analysis. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc.; 2002.
- Srivastava MS. Methods of multivariate statistics. Hoboken, NJ: John Wiley & Sons, Inc.; 2002.
- Greenhouse SW, Geisser S. On methods in the analysis of profile data. Psychometrika. 1959;24:95–112. doi: 10.1007/BF02289823
- Srivastava MS. Profile analysis of several groups. Comm Statist Theory Methods. 1987;16:909–926. doi: 10.1080/03610928708829411
- Fujikoshi Y. Statistical inference for parallelism hypothesis in growth curve model. SUT J Math. 2009;45:137–148.
- Yokoyama T, Fujikoshi Y. A parallel profile model with random-effects covariance structure. J Japan Statist Soc. 1993;23:83–89.
- Okamoto N, Miura N, Seo T. On the distributions of some test statistics for profile analysis in elliptical populations. Amer J Math Management Sci. 2014;26:1–31.
- Maruyama Y. Asymptotic expansions of the null distributions of some test statistics for profile analysis in general distributions. J Statist Plann Inference. 2007;137:506–526. doi: 10.1016/j.jspi.2006.01.010
- Ledoit O, Wolf M. Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann Statist. 2002;30:1081–1102. doi: 10.1214/aos/1031689018
- Srivastava MS. Some tests concerning the covariance matrix in high dimensional data. J Japan Statist Soc. 2005;35:251–272. doi: 10.14490/jjss.35.251
- Fujikoshi Y, Ulyanov VV, Shimizu R. Multivariate statistics: high-dimensional and large-sample approximations. Hoboken (NJ): John Wiley & Sons, Inc.; 2010.
- Hyodo M, Takahashi S, Nishiyama T. Multiple comparisons among mean vectors when the dimension is larger than the total sample size. Comm Statist Simulation Comput. 2014;43:2283–2306. doi: 10.1080/03610918.2012.762387
- Shutoh N, Takahashi S. Profile analysis in high-dimensional data, 12–12. Hiroshima Statistical Research Group, Hiroshima University; 2012.
- Nishiyama T, Hyodo M, Seo T, Pavlenko T. Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices. J Statist Plann Inference. 2013;143:1898–1911. doi: 10.1016/j.jspi.2013.07.008
- Potthoff RF, Roy SN. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika. 1964;51:313–326. doi: 10.1093/biomet/51.3-4.313
- Brunner E, Domhof S, Langer F. Nonparametric analysis of longitudinal data in factorial experiments. Hoboken (NJ): John Wiley & Sons, Inc.; 2002.
- Schott JR. Matrix analysis for statistics. 2nd ed. Hoboken (NJ): John Wiley & Sons, Inc.; 2005.
- Himeno T. Asymptotic expansions of the null distributions for the Dempster trace criterion. Hiroshima Math J. 2007;37:431–454.