I'm looking for some general guidance on where to look if I want to solve this problem I encountered:
I have two unknown distributions- p and q, from the same family of distributions. Just for the discussion, let's assume both distributions are gaussians, so I know how to parameterize them. From the first distribution I have n samples and from the second distribution I have m samples.
I know there are many statistical tests to calculate the distance of the two distributions from their samples. But in this case there's a catch: n >> m.
m is not large enough to try to reliably fit the samples to a distribution. The large difference between the quantity of samples from each distribution creates an uncertainty of the parameters of the distributions, making it harder to calculate a definitive distance. So, in order to make this more well defined, I want to calculate the smallest probable distance between the two distributions.