Re: Why kullback-leibler distance?

In article <443e11f7$1@xxxxxxxxxxxxxx>, David Jones <dajxxx@xxxxxxxxx> wrote:
Herman Rubin wrote:
In article <443a87c6@xxxxxxxxxxxxxx>, David Jones <dajxxx@xxxxxxxxx>
wrote:
kalyan wrote:
Does Kolmogorov-smirnov statistics be used for multivariate
gaussian
distribution. I hope the question makes sense.



The KS measure can be used, but is likely to be difficult to
calculate because of the difficulty in calculating the CDF of the
multivariate gaussian distribution.

Let me add that the distribution of the KS statistic
also under the null hypothesis depends on the jointness
of the distribution, and the asymptotic distribution is
not subject to the usual means of calculation.

OK, but I think/thought the OP was concerned with a measure of
difference between theoretically-known distributions and he wanted the
measure to be symmetric. My comment "because of the difficulty in
calculating the CDF of the multivariate gaussian distribution" was
based on assuming that the KS value would be calculated by evaluating
the two CDFs on a mutivariate grid and extracting the maximum absolute
difference. So, no statistical sample involved in this case.

This might be a good approximation to the statistic, but
how would you know the p-value associated with it? The
distribution is NOT the one-dimensional distribution, but
has a larger tail.

In the case of independence, there are Brownian *** bounds,
but for any kind of dependence, these are inadequate.





--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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