Numéro spécial : Statistique pour les données spatiales et spatio-temporelles et réseau RESSTE
A tutorial on estimator averaging in spatial point process models
[Tutoriel sur la combinaison d’estimateurs dans les modèles de processus ponctuels spatiaux]
Journal de la société française de statistique, Tome 158 (2017) no. 3, pp. 106-123.

Supposons que plusieurs estimateurs concurrents soient disponibles pour estimer le paramètre d’un modèle statistique. L’objectif de la combinaison d’estimateurs est de fournir un nouvel estimateur, combinaison linéaire des estimateurs initiaux, ayant de meilleures propriétés, au sens du coût quadratique, que chaque estimateur initial. Cette contribution fournit une présentation claire et accessible de la méthodologie, et évalue ses performances sur des modèles classiques de processus ponctuels spatiaux. Il apparait clairement que l’estimateur obtenu par combinaison est plus performant que les procédures d’inférence standards pour les modèles considérés. Pour chaque exemple traité, le code nécessaire à l’implémentation avec le logiciel R (qui se résume à quelques lignes) est fourni.

Assume that several competing methods are available to estimate a parameter in a given statistical model. The aim of estimator averaging is to provide a new estimator, built as a linear combination of the initial estimators, that achieves better properties, under the quadratic loss, than each individual initial estimator. This contribution provides an accessible and clear overview of the method, and investigates its performances on standard spatial point process models. It is demonstrated that the average estimator clearly improves on standard procedures for the considered models. For each example, the code to implement the method with the R software (which only consists of few lines) is provided.

Keywords: Aggregation, Averaging, Boolean model, Determinantal point process, Poisson point process, Thomas process
Mot clés : Agrégation, Combinaison, Modèle Booléen, Processus ponctuels déterminantaux, Processus ponctuel de Poisson, Processus de Thomas 
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     title = {A tutorial on estimator averaging in spatial point process models},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {106--123},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {158},
     number = {3},
     year = {2017},
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Lavancier, Frédéric; Rochet, Paul. A tutorial on estimator averaging in spatial point process models. Journal de la société française de statistique, Tome 158 (2017) no. 3, pp. 106-123. http://archive.numdam.org/item/JSFS_2017__158_3_106_0/

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