Testing spatial randomness based on empirical distribution function: A study on lattice data

In this article, we extended the empirical distribution function based test statistic IkIk of Skaug and Tjostheim [1993. Nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591–602] in the time series setting to DnDn for spatial lattice data and derived the asymptotic distribution of the proposed test statistic DnDn under the null hypothesis of spatial independence. The size and power of the proposed test statistic under conditional autoregressive model (CAR) were simulated. We applied DnDn, Moran's I and Geary's c   to the transformed and well-studied sudden infant death syndrome data from North Carolina and found that DnDn produced a much smaller pp-value in testing spatial independence.