From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Sat 03 Jul 2004 - 03:07:06 EST

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https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Jul 03 03:09:47 2004

Date: Sat 03 Jul 2004 - 03:07:06 EST

Have you tried simulating several special cases? The right set of simulations should suggest an answer, which might then lead you to a proof.

hope this helps. spencer graves

Eugene Salinas (R) wrote:

> Thanks. This is sort of what I have been trying to do... but I keep

*> ending up with products of non-independent chi-squares where I am sort
**> of getting stuck. I knew this Theorem just never knew it was called
**> Cochran's Thm. Btw, do you know of a good book that deals with
**> multivariate statistics using vector notation etc. All the books I
**> have seem to be focused on scalar random variables and they don't even
**> mention it.)
**>
**> thanks, eugene.
**>
**>
**> Spencer Graves wrote:
**>
**>> Have you considered Cochran's theorem? (A Google search just
**>> produce 387 hits for this, the second of which
**>> "http://mcs.une.edu.au/~stat354/notes/node37.html" provided details
**>> that might help.) By construction, P is n x n, idempotent of rank k,
**>> so y'Py is chi-square(k). Also, xA is an n-vector in the (rank k)
**>> column space of x; indeed, PxA = [x*inv(x'x)*x]xA = xA. I can't see
**>> the details now but I believe you can write (A'x'y)^2 = y'xAA'x'y as
**>> a weighted sum of k independent chi-squares each with one degree of
**>> freedom (since x and P have rank k), and then get what you want from
**>> the sum of the weights. Then check your result using Monte Carlo.
**>> hope this helps. spencer graves
**>>
**>> Eugene Salinas (R) wrote:
**>>
**>>> Hi everyone,
**>>>
**>>> (This is related to my posting on chi-squared from a day ago. I have
**>>> tried simulating this but I am still unable to calculate it
**>>> analytically.)
**>>>
**>>> Let y be an n times 1 vector of random normal variables mean zero
**>>> variance 1 and x be an n times k vector of random normal variables
**>>> mean zero variance 1. x and y are independent.
**>>>
**>>> Then P is the projection matrix P=x*inv(x'*x)*x'
**>>>
**>>> I need to figure out the covariance
**>>>
**>>> Cov ( y'*P*y , (A'*x'*y)^2 ) where A is a constant of dimension k
**>>> times 1.
**>>>
**>>> thanks, eugene.
**>>>
**>>> ______________________________________________
**>>> R-help@stat.math.ethz.ch mailing list
**>>> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
**>>> PLEASE do read the posting guide!
**>>> http://www.R-project.org/posting-guide.html
**>>
**>>
**>>
**>>
**>>
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
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R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Jul 03 03:09:47 2004

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