Titlebook: Elliptically Contoured Models in Statistics; A. K. Gupta,T. Varga Book 1993 Kluwer Academic Publishers 1993 algebra.matrices.matrix.normal

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Mixtures of Normal Distributions,Muirhead (1982) gave a definition of scale mixture of vector variate normal distributions. Using Corollary 2.7.4.1, the scale mixture of matrix variate normal distributions can be defined as follows (Gupta and Varga, 1992c).

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Characterization Results,In this section, we characterize the parameters of m.e.c. distributions which are invariant under certain linear transformations. First we prove the following lemma.

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https://doi.org/10.1057/9781137477859ese distributions proved to be useful in statistical inference. For example, the Wishart distribution is essential when studying the sample covariance matrix in the multivariate normal theory. Random matrices can also be used to describe repeated measurements on multivariate variables. In this case,

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Time-Varying Electric and Magnetic Fields,own matrix. Moreover, assume that x., i = l,...,n are uncorrelated and their joint distribution is elliptically contoured and absolutely continuous. This model can be expressed as .where X = (x., x.,...,x.); Z = (z., z.,...,z.) is a q × n known matrix; B (p × q) and Σ (p × p) are unknown matrices. A

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Mathematics and Its Applicationshttp://image.papertrans.cn/e/image/307811.jpg

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