A goodness-of-fit test for inhomogeneous spatial Poisson processes
Author: Guan, Yongtao
Source: Biometrika, Volume 95, Number 4, 26 December 2008 , pp. 831-845(15)
Publisher: Oxford University Press
Abstract: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 xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="asn045ilm1.gif"/></inline-formula> that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="asn045ilm2.gif"/></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.
Document Type: Research article
Publication date: 2008-12-26