[R] Testing multidimensional random numbers?

[Hofert Jan Marius]

Dear Statistics-Experts,

Assume you have given a new and untested pseudo-random number  
generator (prng) and you want to test if it "works". The distribution  
function (cdf) from which the prng is supposed to sample is known.  
Further, you are given some finite (large) sample from the prng. If  
the sample is one-dimensional, we can apply the cdf to it and test  
the sample for being realizations of i.i.d. U[0,1]-random variables.  
However, my problem is, that the sample is not one-dimensional but  
multidimensional (say I have 10000 observations from the prng where  
each observation is 100 dimensional). How can I test the prng?
One idea would be to apply the known cdf to the data to obtain a one- 
dimensional sample, but the corresponding theoretical distribution  
function (often called 'probability integral transform') is also not  
known. Is there a simple way (or any way) to test such a prng? Most  
papers I found deal with the standard uniform case, which is of  
course easy to test (Kolmogorov-Smirnov, Anderson-Darling, ...).

Thanks in advance!

Marius

m_hofert at web.de

PS: Sorry, this question is not directly related to R, but I hope you  
can help me anyway.