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Processus ponctuels spatiaux pour l'analyse du positionnement optimal et de la concentration

Abstract : Spatial point processes form a branch of spatial statistic used in various application areas (forestry, geo-marketing, seismology, epidemiology...) and developed by recent theoretical results. We are interested primarily in this thesis to the use of spatial point processes theory for solving optimal positioning problems and for defining new concentration indices based on distances in econometrics. The optimal positioning problem is often written as an optimization problem taking into account geo-referenced data with associated characteristics. We consider that the inputs of the problem are a realization of a spatial point process and solve a stochastic positioning problem more realistic than the deterministic model. Through the study of optimal positioning of a new fire station in the Toulouse area, we introduce a new stochastic approach that gives an indication of the spatial variability of the optimal solution and allows to solve larger problems. The implemented approach is validated by preliminary theoretical results on the asymptotic behavior of empirical solutions. The almost sure convergence of empirical optimal solutions of the case study is obtained in an i.i.d. framework using the Vapnik-Cervonenkis theory. We also obtain the almost sure convergence of empirical optimal solutions, in a more general framework, for a positioning problem derived from the Monge-Kantorovich transport problem.\\ Then we turn attention to concentration indices based on distances in econometrics. These concentration indices can be written as estimators of second order characteristics of marked point processes. We then define a nonparametric estimator of a new characteristic of a spatial marked point process defining a new concentration index improving existing ones. In an infill asymptotic framework, our estimator is asymptotically unbiased.
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https://tel.archives-ouvertes.fr/tel-00465270
Contributor : Florent Bonneu Connect in order to contact the contributor
Submitted on : Friday, March 19, 2010 - 1:31:16 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:07 AM
Long-term archiving on: : Tuesday, June 22, 2010 - 10:44:00 AM

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Florent Bonneu. Processus ponctuels spatiaux pour l'analyse du positionnement optimal et de la concentration. Mathématiques [math]. Université de Toulouse, 2009. Français. ⟨tel-00465270⟩

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