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| HAL: hal-00453102, version 1 |
| arXiv: 1002.0857 |
| Detailed view |  Export this paper |
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| Residuals and goodness-of-fit tests for stationary marked Gibbs point processes |
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| Jean-François Coeurjolly 1, 2Frédéric Lavancier 3 |
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| (2010) |
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| The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. (2005) as an empirical counterpart of the {\it Campbell equilibrium} equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and the asymptotic normality are obtained for a wide class of residuals including the classical ones (raw residuals, inverse residuals, Pearson residuals). Based on these asymptotic results, we define goodness-of-fit tests with Type-I error theoretically controlled. One of these tests constitutes an extension of the quadrat counting test widely used to test the null hypothesis of a homogeneous Poisson point process. |
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| 1: | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
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CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble |
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| 2: | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble |
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| 3: | Laboratoire de Mathématiques Jean Leray (LMJL) |
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CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes |
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| Subject | : | Mathematics/Statistics Statistics/Theory |
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| stationary marked Gibbs point processes – residuals – goodness-of-fit test – quadrat counting test – maximum pseudolikelihood estimator – Campbell Theorem – Georgii-Nguyen-Zessin formula – central limit theorem for spatial random fields |
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| Attached file list to this document: | ||||||||||
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| hal-00453102, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00453102/en/ | |
| oai:hal.archives-ouvertes.fr:hal-00453102_v1 | |
| From: Jean-François Coeurjolly | |
| Submitted on: Wednesday, 3 February 2010 20:39:12 | |
| Updated on: Friday, 19 February 2010 16:15:06 | |
