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A simplified version of Cochran's theorem in mixed linear models
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Tonghui Wang
Published/Copyright:
December 8, 2008
Abstract
For a multivariate normally distributed n × p random matrix Y with mean μ and covariance ΣY = V1⊗Σ1 + V2⊗Σ2, necessary and sufficient conditions, under which Y′WY follows a Wishart distribution, are obtained, where W is a symmetric matrix, V1 and V2 are known nonnegative definite matrices, and Σ1 and Σ2 are unknown nonnegative definite parameter matrices. Several examples are given to illustrate our main results.
Key words.: Cochran's theorem; multivariate normal distributions; necessary and sufficient conditions; matrix quadratic forms; symmetric matrices
Received: 2007-10-12
Published Online: 2008-12-08
Published in Print: 2008-November
© de Gruyter 2008
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Keywords for this article
Cochran's theorem;
multivariate normal distributions;
necessary and sufficient conditions;
matrix quadratic forms;
symmetric matrices
Articles in the same Issue
- Weak solutions for random nonlinear parabolic equations of nonlocal type
- A simplified version of Cochran's theorem in mixed linear models
- On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space. Part 1
- A remark on some random fixed points of multivalued SL-random operators satisfying the nonstrict Opial's property and corrigendum to “Random fixed points of multivalued random operators with property (D)”
- Discrete time approximation of BSDEs driven by a Lévy process
- Transforming random operators into random bounded operators
- A remark on probability distributions and characteristic functionals for random functions of sets
