A goodness-of-fit test for inhomogeneous spatial Poisson processes

We introduce a formal testing procedure to assess the goodness-of-fit of a fitted inhomogeneous spatial Poisson process model. Our method is based on a discrepancy measure function Dc(t; θ̂) that is constructed by using residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and then develop a test statistic based on these properties. Our test statistic has a limiting standard normal distribution so the test can be performed by simply comparing the test statistic with critical values obtained from the standard normal distribution. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example. Some key words: Goodness-of-fit test; Inhomogeneous spatial Poisson process; Residual diagnostics. Short Title. Goodness-of-Fit Test for Poisson Processes.