Titlebook: Elliptically Contoured Models in Statistics and Portfolio Theory; Arjun K. Gupta,Tamas Varga,Taras Bodnar Book 2013Latest edition Springer

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Meals in the Early Christian Worldof a given phenomenon.For example, one emphasizes invariance under quadratic forms, another one uses a general latent structure to define distributions, etc. In this chapter, we deal with matrix variate closed skew normal distributions. Their distributional properties are presented and the extension

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https://doi.org/10.1007/978-1-4614-8154-6Distributions; Elliptical models; Matrix algebra; Multivariate statistical analysis; Quadratic forms; Sta

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https://doi.org/10.1007/978-3-642-81350-4In this chapter, we study how results, similar to Cochran’s theorem can bederived for matrix variate elliptically contoured distributions. We also present several resultson ranks of quadratic forms as well as on distributions of invariant functions of random matrices.

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Ausgangssituation und Grundbegriffe,In this chapter, we characterize the parameters of matrix variate ellipticallycontoured distributions which are invariant under certain linear transformations. Further-more, it is shown that if matrix variate elliptically contoured distributions possess certain properties, they must be normal.

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,Maßregeln zur Verhütung von Waldbränden,Before studying concrete hypotheses, we derive some general theorems. These results are based on Anderson, Fang, and Hsu (.) and Hsu (.).

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Quadratic Forms and Other Functions of Elliptically Contoured MatricesIn this chapter, we study how results, similar to Cochran’s theorem can bederived for matrix variate elliptically contoured distributions. We also present several resultson ranks of quadratic forms as well as on distributions of invariant functions of random matrices.