Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality

References

• Ahmad, M.R. (2014a). A U-statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens-Fisher setting. Ann. Inst. Stat. Math. 66:33–61.
   Web of Science ®Google Scholar
• Ahmad, M.R. (2014b). Location-invariant and non-invariant tests for high-dimensional covariance matrices under normality and non-normality. Technical report, 2014:4, Uppsala University, Sweden.
   Google Scholar
• Ahmad, M.R. (2015). U-tests of general linear hypotheses for a high-dimensional under non-normality and heteroscedasticity. J. Stat. Th. Pr. 9:544–570.
   Web of Science ®Google Scholar
• Ahmad, M.R., Rosen, D. (2015). Tests of covariance matrices for high dimensional multivariate data under non-normality. Commun. Stat.: Th. Me 44(7):1387–1398.
   Web of Science ®Google Scholar
• Ahn, J., Marron, J.S., Muller, K.M., Chi, A.Y. (2007). The high-dimension, low sample size geometric representation holds under mild conditions. Biom 94(3):760–766.
   Google Scholar
• Birke, M., Dette, H. (2005). A note on testing the covariance matrix for large dimension. Stat. Prob. Lett. 74:281–289.
   Web of Science ®Google Scholar
• Chen, S.X., Zhang, L-X., Zhong, P-S. (2010). Tests for high dimensional covariance matrices. J. Am. Stat. Assoc. 105:810–819.
   Web of Science ®Google Scholar
• Dehling, H., Denker, M., Philipp, W. (1984). Invariance principles for von Mises and U-statistics. Z. Wahrsch. verw. Gebiete 67:139–167.
   Web of Science ®Google Scholar
• Denker, M., Keller, G. (1983). On U-statistics and v. Mises’ statistics for weakly dependent processes. Z. Wahrsch verw. Gebiete 64:505–522.
   Web of Science ®Google Scholar
• Fujikoshi, Y., Ulyanov, V.V., Shimizu, R. (2010). Multivariate Statistics: High-dimensional and Large-sample Approximations. New York: Wiley.
   Google Scholar
• Hájek, J., Šidák, Z., Sen, P.K. (1999). Theory of Rank Tests. San Diego: Academic Press.
   Google Scholar
• Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Ann. Math. Stat. 19:293–325.
   Google Scholar
• John, S. (1971). Some optimal multivariate tests. Biom 58:123–127.
   Google Scholar
• Koroljuk, V.S., Borovskich, Y.V. (1994). Theory of U-statistics. Dordrecht: Kluwer Academic Press.
   Google Scholar
• Ledoit, O., Wolf, M. (2002). Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann. Stat. 30:1081–1102.
   Web of Science ®Google Scholar
• Lee, A.J. (1990). U-statistics: Theory and Practice. Boca Raton: CRC Press.
   Google Scholar
• Li, J., Chen, S.X. (2012). Two sample tests for high-dimensional covariance matrices. Ann. Stat. 40(2):908–940.
   Web of Science ®Google Scholar
• Lehmann, E.L. (1999). Elements of Large-Sample Theory. New York: Springe.
   Google Scholar
• Muirhead, R.J. (2005). Aspects of Multivariate Statistical Theory. New York: Wiley.
   Google Scholar
• Nagao, H. (1973). On some test criteria for covariance matrix. Ann. Stat. 1:700–709.
   Web of Science ®Google Scholar
• Pinheiro, A., Sen, P.K., Pinheiro, H.P. (2009). Decomposibility of high-dimensional diversity measures: Quasi-U-statistics, martigales, and nonstandard asymptotics. J. Multivariate Anal. 100:1645–1656.
   Web of Science ®Google Scholar
• Schott, J.R. (2007). A test for the equality of covariance matrices when the dimnsion is large relative to the sample size. Comput. Stat. Data Anal. 51:6535–6542.
   Web of Science ®Google Scholar
• Seber, G.A.F. (2004). Multivariate Observations. New York: Wiley.
   Google Scholar
• Sen, P.K. (2006). Robust statistical inference for high-dimensional data models with applications in genomics. Aust. J. Stat. 35(2& 3):197–214.
   Google Scholar
• Sen, P.K. (2009). High-dimensional discrete statistical models: UIP, MCP and CSI in perspectives (Ch. 1). In: Advances in Multivariate Statistical Methods, Vol. 4 (Statistical Science and Interdisciplinary Research), New Jersey: Wolrd Scientific Publishing.
   Google Scholar
• Sen, P.K. (1974). Weak convergence of generalized U-statistics. Ann. Prob. 2(1):90–102.
   Web of Science ®Google Scholar
• Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. Weinheim: Wiley.
   Google Scholar
• Srivastava, M.S. (2005). Some tests concerning the covariance matrix in high dimensional data. J. Japan Stat. Soc. 35(2):251–272.
   Google Scholar
• Wolfinger, R.D. (1996). Heterogeneous variance: Covariance structures for repeated measures. J. Agr. Biol. Environ. Stat. 1(1):205–230.
   Google Scholar
• van der Vaart, A.W. (1998). Asymptotic Statistics. Cambridge: Cambridge University Press.
   Google Scholar