Re: random matrices: how to generate random correlation matrix?
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 21 Dec 2008 13:19:33 -0500
In article <18776833.1229814194541.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Blow Peep <kentonyee@xxxxxxxxx> wrote:
I want to use Matlab to create NxN random correlation and covariance matrices.
Does random matrix theory give any guidance on how to generate a random covariance matrix that is automatically positive semi definite? Any introductory references? thansk!
Assuming normality, if the columns of a NxT matrix X
are independent samples with covariance matrix QQ'
(any decomposition will do), the matrix XX' can be
written as QA(QA)', where A is a triangular matrix
generated as follows:
a_ij = 0 if j > i,
a_ii is chi with T-i+1 degrees of freedom,
a_ij is normal(0,1) if i > j.
If T < N, stop at column T, only 0's to the right.
This minimizes the number of random variables needed.
--
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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