How to generate two random vectors correlated to three existing vectors

[Lubomir]

Let's have three vectors that are given and cannot change (M, N and O). I have to generate two random vectors X and Y. The correlation that has to be kept is given by the correlation matrix C. The correlation matrix show the correlation between all the vectors (M, N, O , X and Y).

Does anyone know, how to achive this in general? Some kind of SAS code would help as well.

 

[BGM]

Maybe you are talking about

http://en.wikipedia.org/wiki/Partial_correlation

But in general you will need to find the conditional joint pdf for the generation.

 

[Lubomir]

Actually no. Partial correlation is a theory for completely different things. It does not help generating new random variables.

 

[BGM]

So as said before do you know / can you specify the conditional joint pdf

\( f_{X, Y|M, N, O}(x, y|m, n, o) \)

And can it be completely characterized by a given correlation matrix (i.e. is it the only parameter of the distribution)?