Bootstrap testing for first-order stationarity on irregular windows in spatial point patterns

Abstract

Kernel smoothing is commonly used in spatial point patterns to construct intensity plots. Kernels allow for visually and subjectively inferring on first-order stationarity. Formal objective tests exist for testing first-order stationarity that assume independence of spatial regions. We propose to extend inference for first-order stationary by using bootstrapping in existing hypothesis tests to deal with the violation of independence. More specifically we compare Poisson intensities from bootstrapped spatial quadrat samples, providing a test for first-order stationarity without violating the assumption of independence of the tests. Five hypothesis testing methods are investigated. The choice of grid mesh size and window shape used in these tests is discussed and guidance is provided through testing the power of the tests. The application considers the household locations in rural villages in Northern Tanzania as an unmarked point pattern. A clear effect of the village sizes on the relation between grid mesh size and confidence intervals of bootstrap sampling is shown. We conclude that bootstrapping provides a novel contribution to inference of first-order stationarity for spatial point patterns.