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I want to study a point pattern using cumulative NND (Nearest Neighbor Distance) "G" function . The main task is to test H0: the point process is compatible with a null model (can be CSR (complete spatial randomness) or other)

I have see two options:

  1. Generate N point pattern under the null model. Calculate G function for all the patterns, calculate G function for the data. Run 2 sample KS test on both these G functions.

  2. Generate N point pattern under the null model. Calculate G function for each pattern, calculate G function for the data. And use test which accounts for CE (like MAD (Maximum Absolute Deviation) or DCLF ( Diggle-Cressie-Loosmore-Ford) test)

Which way is the most appropriate (and why) for testing hypotheses based on summary functions such as distributions of NNDs?

Thanks!

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  • $\begingroup$ Our policy is to spell out abbreviations on first use unless they've become a commonly used word in their own right (like ANOVA); in this case, NND, CSR MAD, CE and DCLF all need to be explained, and it might help to identify what a G function is. Strictly speaking KS should also be fixed as well, but you at least have the tag for that, so people might guess it. $\endgroup$ – Glen_b -Reinstate Monica Sep 9 '17 at 3:55
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Option 2 is the one that is commonly used and recommended. This is a formal Monte Carlo test with well established theory. You can read about the theory and how to do it in practice in Spatial Point Patterns: Methodology and Applications with R by Baddeley, Rubak and Turner (disclaimer: I'm one of the authors).

I think one of the problems with option 1 is that the asymptotic distribution of the classical Kolmogorov-Smirnov test statistic assumes independence between the observations. When observations are e.g. nearest neighbours in the same point pattern you don't have independence.

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