Convex and non-convex regularization methods for spatial point processes intensity estimation

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

1 FIGAL - Fiabilité et Géométrie Aléatoire
2 SVH - Statistique pour le Vivant et l’Homme

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood and logistic regression likelihood. We provide general conditions on the spatial point processes and on penalty functions which ensure consistency, sparsity and asymptotic normality. We discuss the numerical implementation and assess finite sample properties in a simulation study. Finally, an application to tropical forestry datasets illustrates the use of the proposed methods.

Mots clés: Campbell theorem; Estimating function; Feature selection; Logistic regression likelihood; Penalized regression; Poisson likelihood

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]; Théorie [stat.TH]

Achmad Choiruddin, Jean-François Coeurjolly, Frédérique Letué. Convex and non-convex regularization methods for spatial point processes intensity estimation. Electronic Journal of Statistics , 2018, 12 (1), pp.1210-1255. ⟨10.1214/18-EJS1408⟩. ⟨hal-01484779v2⟩