Kolmogorov-Smirnov Test as a Measure of Statistical Distance Between Two Dependent Probability Distributions Much has been asked on CV regarding the Kolmogorov-Smirnov (KS) test, but not in the context I need.
I'm wondering how feasible it would be to employ KS as a measure of distance between two dependent PDFs, as opposed to using something like the Kullback-Leibler (KL) divergence, cross entropy, or Hellinger distance
Say I partition a distance matrix $D$ into two parts, $A$ and $B$. If I then plot $A$ and $B$ as kernel density estimates, I'd like to know how much their resulting curves overlap (or not). By overlap, I mean the two curves intersect at one or multiple points.
Details
In my case, $A$ comprises pairwise distances for a sample of individuals of a particular species, while $B$ contains pairwise distances between individuals for all other species.
So, if I had 3 species in total $\{L, M, N\}$, where I sample 10 individuals of $L$, 3 of $M$, and 2 of $N$, $A$ would contain all  $\binom{10}{2}$ pairwise distances for species $L$, whereas $B$ would contain $\binom{5}{2}$ pairwise distances for individuals of species $M$ and $N$. This scheme would then be repeated for species $M$ and $N$.
Note $A$ and $B$ would not necessarily be conformable, which is a requirement for something like the KL divergence. By conformable, $A$ and $B$ should contain the sample number of elements. At least, that's what I gauge from R when it indicates
arrays are non-conformable

when I attempt to compute cross entropy.
I could always employ techniques like smoothing to try to get around this, but perhaps there's a simpler way.
I'm thinking the KS test could be used as follows:
$H_0$: $A$ = $B$ (overlap}
$H_1$: $A$ $\neq$ $B$ (separation}
Large values of the test statistic (or small $p$-value) would give strong evidence that the two distributions do not overlap.

Using the $p$-value is not ideal because it depends on sample size and doesn't estimate anything, but you can use the test statistic. This is just the maximum vertical separation between the CDFs, the uniform/supremum norm on CDFs, which is quite widely studied.
