Abstract
Abstract : A natural test of complete spatial randomness (CSR) for spatial point patterns based on the inter-event distance distribution has poor power against even obvious departures. We propose two modifications of the test statistic to improve its power. The first is a reweighting to put more emphasis on deviations from CSR at shorter distances. The second is to apply the theory of the projection of U-statistics to lower the variance of the test statistic under the null hypothesis. In examples where previous methods based on inter-event distances failed to detect alternatives, we show that these modifications to the test statistic allow the detection of departures from CSR. Simulations of stationary and near stationary alternatives to CSR further illustrate the improvement in inter-event distance tests of CSR gained from weighting and projection. In addition, we propose two simple modifications to the graphical presentation of the empirical inter-event distance distribution to elucidate alternatives. (AN)
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