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Abstract: The inspection of residuals is a fundamental step to investigate the qualityof adjustment of a parametric model to data. For spatial point processes, theconcept of residuals has been recently proposed by Baddeley et al. 2005 as anempirical counterpart of the {\it Campbell equilibrium} equation for markedGibbs point processes. The present paper focuses on stationary marked Gibbspoint processes and deals with asymptotic properties of residuals for suchprocesses. In particular, the consistency and the asymptotic normality areobtained for a wide class of residuals including the classical ones rawresiduals, inverse residuals, Pearson residuals. Based on these asymptoticresults, we define goodness-of-fit tests with Type-I error theoreticallycontrolled. One of these tests constitutes an extension of the quadrat countingtest widely used to test the null hypothesis of a homogeneous Poisson pointprocess.



Author: Jean-François Coeurjolly GIPSA-lab, LJK, Frédéric Lavancier LMJL

Source: https://arxiv.org/







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