# test for correlation of a multivariate non-normal distribution

Assume I want to generate a sample of n-dimensional vector $z$ with a given correlation matrix $Corr(z)=R$. Some of the margins of its distribution are not normal (if you're interested here's the motivation behind my question), i.e. $z$ doesn't follow the multivariate normal distribution.
Let's assume that I have some imperfect method and I want to check if the sample correlation matrix is close to the theoretical one, i.e. I'd like to test the null hypothesis $H_0:R_{sample}=R$ vs $H_1:R_{sample}\neq R$
How can I do it?

• See this answer - the method of Ruscio and Kaczetow (2008) can help you creating the data matrix stats.stackexchange.com/a/43230/6082 – Felix S Jan 14 '13 at 8:51
• I don't think so. But the code can be found here. – Felix S Jan 15 '13 at 6:13
• Thanks for the code. However, I still would like to test the hypothesis if the sample generated with this code (or with any other) has the given correlation matrix R (i.e. H_0:R_sample=R, H_1: not H_0). What do you think how can this be achieved? – Max Li Jan 16 '13 at 15:46
• I am a civil engineer specialized in probabilistis geotechnics. I not know if it is of any interest, but I have developed an algorith for the random drawing of not-normal multivariate statistical distribution functions. I keep it now secret, but when I think that the time is there I shall publish it. Thank you for your interest, Henk Bakker, Netherlands. – user130118 Sep 5 '16 at 19:53
• It sounds like you might be talking about using a Gaussian copula model? I am not very knowledgeable in this area, but e.g. a Google Scholar search turns up this reference, which may be useful. Copulas are very common in finance, so you may also check on the Quant site. – GeoMatt22 Sep 5 '16 at 20:38