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

2017/03/07 by Achmad Choiruddin, Jean-François Coeurjolly, Frédérique Letué · 31 citations
Environmental Science · Mathematics · #Domain (mathematical analysis) #Feature selection #Intensity (physics) #Oracle #Point (geometry) #Point process #Point processes and geometric inequalities #Poisson distribution #Poisson sampling #Regular polygon #Regularization (linguistics) #Soil Geostatistics and Mapping #Statistical Methods and Inference #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.1214/18-ejs1408

published in Electronic Journal of Statistics 12(1) (Institute of Mathematical Statistics)

arxiv created 2017/03/07 · openalex created_date 2017/05/12 · openalex publication_date 2018/01/01 · arxiv updated 2018/07/12 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• Statistical Inference and Simulation for Spatial Point Processes
• Nearly unbiased variable selection under minimax concave penalty
• High-dimensional variable selection
• One-step sparse estimates in nonconcave penalized likelihood models
• Pathwise coordinate optimization
• Least angle regression
• On the adaptive elastic-net with a diverging number of parameters