Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation

Abstract

Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on inhomogeneous parametric forms of these functions assumed to depend on a certain number of spatial covariates. When this number of covariates is large, we are faced with a high-dimensional problem. This paper provides an overview of these questions and existing solutions based on regularizations.

19 pages, 2 figures

References in corpus (2)

• On the adaptive elastic-net with a diverging number of parameters
• Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model