Properties of residuals for spatial point processes.

Baddeley, A.; Møller, J.; Pakes, A.

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.

STOCHASTIC processes; DISTRIBUTION (Probability theory); MARTINGALES (Mathematics); PROBABILITY theory; PARAMETERS (Statistics); RATIONAL equivalence (Algebraic geometry); STATISTICAL correlation; GRAPHIC methods in statistics

Annals of the Institute of Statistical Mathematics, 2008, Vol 60, Issue 3, p627

0020-3157

Academic Journal

10.1007/s10463-007-0116-6