There are several (lets say N) sets of randoms (300 random variables each). How can we check that all these sets came from the same superset (N*300). Everything is simple if we have only a pair - we can just use a Kolmogorov-Smirnov test.
Is KS test still applicable (each vs each) for such test or there is another method that can give us a cumulative result showing that all the set follow the same probability function?
You might find useful the Bohm & Hornik's paper "A Kolmogorov-Smirnov Test
for r Samples" (http://epub.wu.ac.at/2960/1/Report105.pdf).
Hope this helps
Dear Edgar, thank you very much! This paper looks really promising.
Dear Mikhail,
The answer does somewhat depend on the way in which you wish to evaluate the equivalency of distributions. Obviously if you are willing and able to specify a distribution of interest more powerful tests the KS are available. Less obviously there are possibilities like comparing the distribution of eigenvalues from the potentially related matrices. Depending on the size of the matrices, you can also get some milage looking at fractional compression coefficients or other possibilities.
Dear Bruce,
Thank you for the interesting answer. Unfortunately the shape of distribution is unknown. In this case we have indeed a sequence of random numbers with no respect to any distribution function. These numbers can be fitted by a stable distribution, but the problem is that the size of each set is small (300 numbers) and such fitting doesn't guarantee satisfactory results.
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