On Wed, 18 Sep 2002 19:31:02 +0000 (UTC), Ronald Bloom
<[EMAIL PROTECTED]> wrote:
>
> One has M>p multiple measurments of a p-dimensional random vector.
>
> The objective is to build up, from these M measurements, an
> estimate S of the "true" covariance matrix C.
>
> This sample covariance is intended to be used in the standard
> role in the "hotelling" quadratic form
>
> D = X'*inv(S)*X
>
> in order to make standard inferential tests on subsequent p-dimensional
> random vectors X, (drawn from the putatively stable process from
> which the sample covariance was estimated), subject to the
> standard assumptions.
>
> For standard inference on D to make any sense, D must be non-negative,
> for all X.
>
> Question is:
>
> I am concerned about the positive definiteness of the form D
> being robust with respect to sampling.
>
[ snip - redundant questioning ]
Any covariance matrix computed on full data is assured to be
non-negative definite.
That is why the multivariate procedures often assume
"list-wise deletion" of cases -- there's not any worry about
frankly inconsistent correlations.
When I was 21, before I took real stat courses, I argued
that you should be able to *try* to use matrices based on
different Ns -- and even, use covariances based on
possibly-inconsistent estimates of variances.
That is: today, with more experience, I think
I *can* imagine an odd data circumstance (one with
small Rs) where it would be useful estimate the Rs from
cov(XY)/ sqrt[var(X)var(Y)]
where each var() and covar() was based on its own
most-complete estimate from the data.
- Nobody will generally want to use this estimator since
they don't know what to do in the cases where it computes
to something greater than 1.0.
Hope this helps.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
