# Multi-dimensional goodness of fit

I have two (soon to be three) dimensional spatial data and I what to compare the goodness of fit between my model and reality. As the data is continuous and not categorial I can't really use the Chi-squared test. I have considered trying to determine the actual error on my measurements and use that as the denominator in the statistic as opposed to the usual Poisson approximation. I have also tried a 2D KS test, I have two issues here, it is rather slow and if I go to three dimensions the number of ways of defining the CDF becomes somewhat prohibitive. My other issue that I don't really know what the answer means beyond that fact that anything that doesn't come back in standard form is very good agreement.

Are there any other goodness of fit tests that are good for higher dimensions? Is Cramer von Mises any better the KS in lots of dimensions, I haven't tried but I assumed it would have the same limitations?

• Is there any example for 2d chi square? I didn't find too many resources about that, for example, this post is only about univariate distribution, itl.nist.gov/div898/handbook/eda/section3/eda35f.htm. Dec 22, 2015 at 6:02