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 <inline-formula><inline-graphic xlink:href="asn045ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of <inline-formula><inline-graphic xlink:href="asn045ilm2.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> 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. Copyright 2008, Oxford University Press.