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

Achmad Choiruddin, Jean François Coeurjolly, Frédérique Letué

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1210-1255
Number of pages46
JournalElectronic Journal of Statistics
Volume12
Issue number1
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Campbell theorem
  • Estimating function
  • Feature selection
  • Logistic regression likelihood
  • Penalized regression
  • Poisson likelihood

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