Not many people know this (or need to know it), but it's all in
Mardia/Kent/Bibby in gory generality.
In the special case of normality (p. 92, Exercise 3.4.17c): if s is
covar(x,y), then cov[var(x),var(y)] is 2s^2/sqrt(n).
Personally I prefer Exercise 3.2.4c (p.86) which is completely useless but
nice and general and just uses a straightforward conditioning argument.
See also Theorem 4.1.1 (p.98), which generalizes Cramer-Rao.
Best Regards
JOHN BIBBY aa42/MatheMagic
1 Straylands Grove, York YO31 1EB (01904-330-334)
All statements are on behalf of aa42.com Limited, a company wholly owned by
John Bibby and Shirley Bibby. See www.aa42.com/mathemagic and
www.mathemagic.org
-----Original Message-----
From: A UK-based worldwide e-mail broadcast system mailing list
[mailto:[log in to unmask]] On Behalf Of Margaret MacDougall
Sent: 23 April 2007 14:47
To: [log in to unmask]
Subject: Expectation of the product of two sample variances
Hello
I would like to obtain an approximation to the expectation of the product
of two sample variances, where in particular:
a) the two sample variances are not independent
and
b) it can be assumed that in each case, the sample variance is calculated
over a Normally distributed sample
Perhaps some work has already been done on estimating the distribution for
the above product, in which case the expectation could be derived on the
basis of this work. Does anyone know of any such work or can you suggest
another way to approximate the expectation under assumptions a) and b)?
Many thanks for your interest in this problem.
Best wishes
Margaret
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