Spatial point processes intensity estimation with a diverging number of covariates

Achmad Choiruddin (1) , Jean-François Coeurjolly (2) , Frédérique Letué (3)

1 Department of Mathematical Sciences [Aalborg]
2 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
3 SVH - Statistique pour le Vivant et l’Homme

Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the number of covariates diverges as the domain of observation increases. In particular, we consider estimating equations based on Campbell theorems derived from Poisson and logistic regression likelihoods regularized by a general penalty function. We prove that, under some conditions, the consistency, the sparsity, and the asymptotic normality are valid for such a setting. We support the theoretical results by numerical ones obtained from simulation experiments and an application to forestry datasets.

Mots clés: estimating equation; regularization method; variable selection; high dimensional regression; Campbell formula

Domaines: Statistiques [math.ST]

Achmad Choiruddin, Jean-François Coeurjolly, Frédérique Letué. Spatial point processes intensity estimation with a diverging number of covariates. 2017. ⟨hal-01672825⟩