An alternative proof for a version of cochran's theorem under elliptical settings |
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| Authors: | Tonghui Wang Ruichan He |
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| Institution: | 1. New Mexico State University , Las Cruces, USA;2. North west University , Xian, China |
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| Abstract: | For an elliptically contoured n × p random matrix Y with mean μ and covariance proportional to ∑Y, the necessary and sufficient conditions, under which (Y?μ)′W(Y?μ) with nonnegative definite W is generalized Wishart distributed, are obtained by using the higher moments of Y. This version of Cochran's theorem is general as the assumptions on ∑Y=A?∑ with nonnegative definite A and ∑, P(Y?μ)=0, and P(Y≠μ)<1 have been relaxed. An example on two way balanced mixed models is given for illustration ot our main results. |
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