Cochran's Theorem - Alternative Formulation

Alternative Formulation

The following version is often seen when considering linear regression. Suppose that is a standard multivariate normal random vector (here denotes the n-by-n identity matrix), and if are all n-by-n symmetric matrices with . Then, on defining, any one of the following conditions implies the other two:

  • (thus the are positive semidefinite)
  • is independent of for

Read more about this topic:  Cochran's Theorem

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