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I am using Mallow's Distance (normalized Earth Mover's Distance) to characterize the similarity between two histograms. This is working very well, but I would like to identify a specific cut-off where the distance represents a statistically significant value. Effectively what I would like to do is perform a hypothesis test regarding the similarity or non-similarity of the histograms at a certain level of significance.

I don't seem to be having much luck finding an explanation of how to determine the associated p-value.

Any/all pointers to an explanation of how to determine the p-value would be greatly appreciated.

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If I understand it right, Mallows distance is not distribution free ... or even scale free.

You would need to specify your null in such a way that the distribution of the test statistic is determined, or at least approximately so.

Then I'd probably just do it by simulation, but asymptotic tests exist, it seems:

e.g. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.5824

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  • $\begingroup$ I had not seen this particular reference; it's a bit more helpful than the others in this area. Could you provide some insight into how you might do this via simulation (using histograms)? Thanks! $\endgroup$
    – Aengus
    Commented May 23, 2013 at 16:35
  • $\begingroup$ Once you have the null pinned down enough that the null distribution is defined, you simulate many samples of data according to the null, and then calculate the distribution of your test statistic. $\endgroup$
    – Glen_b
    Commented May 23, 2013 at 22:31

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