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

作者：Choiruddin Achmad^*; Coeurjolly Jean Francois; Letue Frederique

来源：Electronic Journal of Statistics, 2018, 12(1): 1210-1255.

DOI：10.1214/18-EJS1408

• Campbell theorem
• estimating function
• feature selection
• logistic regression likelihood
• penalized regression
• Poisson likelihood

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem. In particular, we consider two classical functions: the Poisson likelihood and the logistic regression likelihood. We provide general conditions on the spatial point processes and on penalty functions which ensure oracle property, consistency, and asymptotic normality under the increasing domain setting. We discuss the numerical implementation and assess finite sample properties in simulation studies. Finally, an application to tropical forestry datasets illustrates the use of the proposed method.

• 出版日期2018