[R] A subject related question

[Bill.Venables at csiro.au]

Multivariate normal distributions with PSD variance matrices occur all the time.

The most common example in practice would probably be the distribution of the vector of residuals from a normal regression.  It has a degenerate distribution wrt R^n because it is subject to p linear restrictions.

Another common one is the variance matrix of the multinomial distribution, which is singular since the frequencies are subject to a sum constraint \sum f = n.  This is not a multivariate normal distribution, but becomes arbitrarily close to one as the number of trials increases by the multivariate central limit theorem.

Bill Venables. 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Jonathan Beokhokhei
Sent: Sunday, 17 October 2010 4:17 AM
To: r-help at r-project.org
Subject: [R] A subject related question

Dear friends, please allow me a naive subject oriented question at this moment. I was wondering whether VCV matrix for some multivariate normal distribution can be PSD (which I always thought must be PD).

I came across that point as I was working on some sample distribution of some statistic which involves population correlation matrix. As correlation matrix always a PSD, it seems that that sample distribution (that is asymptotically normal) comes with some vcv matrix which is PSD.

Can somebody help me to sort this out?

warm thanks

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