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

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 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.
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Submitted on : Friday, August 24, 2018 - 4:24:17 PM
Last modification on : Monday, December 14, 2020 - 3:40:12 PM
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Achmad Choiruddin, Jean-François Coeurjolly, Frédérique Letué. Convex and non-convex regularization methods for spatial point processes intensity estimation. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (1), pp.1210-1255. ⟨10.1214/18-EJS1408⟩. ⟨hal-01484779v2⟩

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