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-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Jonathan Beokhokhei Sent: Sunday, 17 October 2010 4:17 AM To: r-help@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 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
