Adaptive lasso and Dantzig selector for spatial point processes intensity estimation

TL;DR

This paper extends adaptive lasso and Dantzig selector methods to spatial point process intensity estimation, providing new procedures, computational methods, and asymptotic analysis for high-dimensional covariate settings.

Contribution

It introduces adaptive versions of lasso and Dantzig selector for spatial point processes, with theoretical, computational, and asymptotic developments for increasing parameter dimensions.

Findings

Both procedures perform well in simulations.

The methods are effective on real spatial data.

Asymptotic results support their theoretical validity.

Abstract

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 an original setting where the number of parameters, i.e. the number of spatial covariates considered, increases with the expected number of data points. Both procedures are compared theoretically, in a simulation study, and in a real data example.