P. Juan Verdoy, C. Díaz-Ávalos, J. Mateu Mahiques

When dealing with general multidimensional point processes containing the spatial locations, the temporal occurrence, possible marks attached to each location and finally external covariates defined in the region where the process exists, it is not only interesting but also crucial testing for the condition of separability amongst any subset of the point process components. By separability we mean a multiplicative form for the conditional intensity allowing for individual component estimation. Following previous approximations to this problem, we focus on the conditional intensity function by considering nonparametric kernel-based estimators. Our approach calculates thinning probabilities under the conditions of separability and non-separability and compares them through divergence measures. We develop the statistical properties of our tests under a variety of practical scenarios. An application on modelling the spatio-temporal first-order intensity of forest fires is also developed.

Palabras clave: conditional intensity function multidimensional spatial point processes separability

F. J. Esquivel Sánchez, J. M. Angulo Ibáñez

R. Giraldo Henao, J. Mateu Mahiques, A. Reyes Lizarazo