TY - JOUR
T1 - Properties of residuals for spatial point processes
AU - Baddeley, Adrian
AU - Møller, J.
AU - Pakes, Anthony
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 - 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 -