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Convex and non-convex regularization methods for spatial point processes intensity estimation. (English) Zbl 06864490
Summary: 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.

MSC:
62H11 Directional data; spatial statistics
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62J07 Ridge regression; shrinkage estimators (Lasso)
65C60 Computational problems in statistics (MSC2010)
62P12 Applications of statistics to environmental and related topics
Software:
spatstat; glmnet; R; sparsenet
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