Adaptive lasso and Dantzig selector for spatial point processes intensity estimation

Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive versions of these procedures, develop efficient computational methodologies and derive asymptotic results for a large class of spatial point processes under the setting where the number of parameters, i.e. the number of spatial covariates considered, increases with the volume of the observation domain. Both procedures are compared theoretically and in a simulation study.