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Estimating and testing a structured covariance matrix for three-level multivariate data. (English) Zbl 1216.62095

Summary: This article considers an approach to estimating and testing a new Kronecker product covariance structure for three-level (multiple time points \((p)\), multiple sites \((u)\), and multiple response variables \((q))\) multivariate data. Testing of such covariance structure is potentially important for high dimensional multi-level multivariate data. The hypothesis testing procedure developed in this article can not only test the hypothesis for three-level multivariate data, but also can test many different hypotheses, such as blocked compound symmetry, for two-level multivariate data as special cases. The tests are implemented with two real data sets.

MSC:

62H15 Hypothesis testing in multivariate analysis
62H12 Estimation in multivariate analysis
15A99 Basic linear algebra
65C60 Computational problems in statistics (MSC2010)
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References:

[1] DOI: 10.1214/aoms/1177729698 · Zbl 0042.38203
[2] DOI: 10.1080/03610929108830562 · Zbl 0751.62027
[3] DOI: 10.1016/S0378-3758(01)00235-X · Zbl 1044.62059
[4] DOI: 10.1080/00949659908811970 · Zbl 0960.62056
[5] DOI: 10.1080/03610929408831436 · Zbl 0875.62274
[6] Johnson R. A., Applied Multivariate Statistical Analysis., 6. ed. (2007) · Zbl 1269.62044
[7] DOI: 10.1016/j.jmva.2006.06.002 · Zbl 1112.62057
[8] DOI: 10.1016/j.jspi.2008.11.013 · Zbl 1162.62059
[9] DOI: 10.1016/j.spl.2005.04.020 · Zbl 1071.62052
[10] DOI: 10.1080/02664760120011626 · Zbl 0991.62038
[11] Rao C. R., Curr. Sci. 14 pp 66– (1945)
[12] Rao C. R., Sankhy 12 pp 229– (1953)
[13] DOI: 10.1006/jmva.2001.2009 · Zbl 1011.62011
[14] DOI: 10.1002/sim.2320
[15] DOI: 10.1002/bimj.200510192
[16] Roy A., Proc. Amer. Statist. Assoc. Statist. Comput. Sec. pp 2157– (2007)
[17] Roy A., J. Appl. Statist. Sci. 12 pp 91– (2003)
[18] DOI: 10.1016/j.stamet.2005.07.003 · Zbl 1248.62092
[19] Roy A., Proc. Statist. Data Anal. Sect., Paper 199 pp 1– (2005)
[20] DOI: 10.1201/9781420010923.ch11
[21] DOI: 10.1007/s11634-007-0013-0 · Zbl 1182.62142
[22] DOI: 10.1016/j.spl.2008.01.066 · Zbl 1147.62343
[23] DOI: 10.1111/j.0006-341X.2002.00521.x · Zbl 1210.62074
[24] DOI: 10.1002/sim.1887
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