On 16/10/2010 2:17 PM, Jonathan Beokhokhei wrote:
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?
I suppose it depends on your definitions, but the following gives a
bivariate normal with a singular covariance matrix:
X1 ~ N(0,1)
Y1 = X1
Then the pair (X1, Y1) is bivariate normal and singular. It has no
density with respect to Lebesgue measure on R^2.
Duncan Murdoch
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