Annals of the Institute of Statistical Mathematics

, Volume 60, Issue 3, pp 627–649

Properties of residuals for spatial point processes

Article

DOI: 10.1007/s10463-007-0116-6

Cite this article as:
Baddeley, A., Møller, J. & Pakes, A.G. Ann Inst Stat Math (2008) 60: 627. doi:10.1007/s10463-007-0116-6

Abstract

For any point process in \({\mathbb{R}}^d\) that has a Papangelou conditional intensity λ, we define a random measure of ‘innovations’ which has mean zero. When the point process model parameters are estimated from data, there is an analogous random measure of ‘residuals’. We analyse properties of the innovations and residuals, including first and second moments, conditional independence, a martingale property, and lack of correlation. Some large sample asymptotics are studied. We derive the marginal distribution of smoothed residuals by solving a distributional equivalence.

Keywords

Distributional equivalenceGeorgii-Nguyen-Zessin formulaGibbs point processSet-indexed martingalePapangelou conditional intensityPearson residualsScan statisticSmoothed residual field

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2007

Authors and Affiliations

  1. 1.School of Mathematics and Statistics M019University of Western AustraliaNedlandsAustralia
  2. 2.CSIRO Mathematical and Information SciencesWembleyAustralia
  3. 3.Department of Mathematical SciencesAalborg UniversityAalborg ØDenmark