Printed in Great Britain A goodness-of-fit test for inhomogeneous spatial Poisson processes

We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function Dc(t; θ̂) that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example