Regularized Poisson and logistic methods for spatial point processes intensity estimation with a diverging number of covariates

Abstract : Many methods for estimating parametrically the intensity function for inhomogeneous spatial point processes are available in the literature. Almost all studies consider the setting where the number of covariates is moderate. More and more applications involve a large number of covariates. Our study considers feature selection procedures based on convex and non-convex regularization techniques to deal with such data. We propose regularized versions of estimating equations based on Campbell theorem derived from Poisson and logistic regression likelihoods. We investigate theoretical and computational aspects. In particular, from a theoretical point of view, we consider asymptotic properties which make our results available for several penalty functions and large classes of spatial point processes
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Submitted on : Friday, June 16, 2017 - 10:48:29 AM
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Achmad Choiruddin, Jean-François Coeurjolly, Frédérique Letué. Regularized Poisson and logistic methods for spatial point processes intensity estimation with a diverging number of covariates. 19th workshop on Stochastic Geometry, Stereology and Image Analysis (SGSIA), May 2017, Luminy, France. ⟨hal-01540246⟩

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