Properties of residuals for spatial point processes

Adrian Baddeley, J. Møller, Anthony Pakes

Research output: Contribution to journalArticle

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Abstract

For any point process in Rd 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.
Original languageEnglish
Pages (from-to)627-649
JournalAnnals of the Institute of Statistical Mathematics
Volume60
Issue number3
DOIs
Publication statusPublished - 2008

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