Properties of residuals for spatial point processes

A. Baddeley, Jesper Møller, A. G. Pakes

Research output: Contribution to journalJournal articleResearchpeer-review

38 Citations (Scopus)

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
JournalAnnals of the Institute of Statistical Mathematics
Volume60
Issue number3
Pages (from-to)627-649
ISSN0020-3157
DOIs
Publication statusPublished - 2008

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Spatial Point Process
Random Measure
Point Process
Conditional Independence
Marginal Distribution
Martingale
Process Model
Equivalence
Moment
Zero
Innovation

Cite this

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Properties of residuals for spatial point processes. / Baddeley, A.; Møller, Jesper; Pakes, A. G.

In: Annals of the Institute of Statistical Mathematics, Vol. 60, No. 3, 2008, p. 627-649.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Properties of residuals for spatial point processes

AU - Baddeley, A.

AU - Møller, Jesper

AU - Pakes, A. G.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1007/s10463-007-0116-6

DO - 10.1007/s10463-007-0116-6

M3 - Journal article

VL - 60

SP - 627

EP - 649

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 3

ER -