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 I k 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 D n for spatial lattice data and derived the asymptotic distribution of the proposed test statistic D n 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 D n , Moranʹs I and Gearyʹs c to the transformed and well-studied sudden infant death syndrome data from North Carolina and found that D n produced a much smaller p -value in testing spatial independence.