Re: Distribution of certain quadratic form
From: Barry Quinn (bquinn_at_efs.mq.edu.au)
Date: 11/19/04
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Date: Fri, 19 Nov 2004 11:49:37 +1100
There is not enough information. If the Gaussian distributions all have mean
0 and variance 1, then your quantity
has a chisquare distribution with M degrees of freedom. If the means and
variances are arbitrary, it will be very
difficult to work out the distribution. I hope this wasn't a homework
problem. To find the distribution, work out the
distribution of A'x conditional on x, then the distribution of
A'x/(x'x)^(1/2).
Barry Quinn
"saksan" <saksan@gmail.com> wrote in message
news:8b044514.0411181126.546e20a3@posting.google.com...
> Hi,
>
> Does anybody know the distribution of
>
> x'AA'x/(x'x) ?
>
> (where A is NxM matrix with i.i.d Gaussian distributed elements
> and x is Nx1 vector with i.i.d Gaussian distributed elements
> and A and x are independent)
>
> Any pointer is appreciated. Thank you.
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