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 
@article{JSFS_2017__158_3_106_0,
     author = {Lavancier, Fr\'ed\'eric and Rochet, Paul},
     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},
     mrnumber = {3720132},
     zbl = {1378.62094},
     language = {en},
     url = {http://www.numdam.org/item/JSFS_2017__158_3_106_0/}
}
TY  - JOUR
AU  - Lavancier, Frédéric
AU  - Rochet, Paul
TI  - A tutorial on estimator averaging in spatial point process models
JO  - Journal de la société française de statistique
PY  - 2017
SP  - 106
EP  - 123
VL  - 158
IS  - 3
PB  - Société française de statistique
UR  - http://www.numdam.org/item/JSFS_2017__158_3_106_0/
LA  - en
ID  - JSFS_2017__158_3_106_0
ER  - 
%0 Journal Article
%A Lavancier, Frédéric
%A Rochet, Paul
%T A tutorial on estimator averaging in spatial point process models
%J Journal de la société française de statistique
%D 2017
%P 106-123
%V 158
%N 3
%I Société française de statistique
%U http://www.numdam.org/item/JSFS_2017__158_3_106_0/
%G en
%F JSFS_2017__158_3_106_0
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://www.numdam.org/item/JSFS_2017__158_3_106_0/

[1] Bates, John M; Granger, Clive WJ The combination of forecasts, Operations Research, Volume 20 (1969) no. 4, pp. 451-468

[2] Biscio, Christophe Ange Napoléon; Lavancier, Frédéric Contrast estimation for parametric stationary determinantal point processes., Scandinavian Journal of Statistics, Volume 44 (2017) no. 1, pp. 204-229 | MR | Zbl

[3] Baddeley, A.; Rubak, E.; Turner, R. Spatial Point Patterns: Methodology and Applications with R., Chapman and Hall/CRC Press, London, 2015

[4] Baddeley, A.; Turner, R. Modelling spatial point patterns in R , Journal of Statistical Software, Volume 12 (2005) no. 6, pp. 1-42

[5] Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H. Aggregation for Gaussian regression, Ann. Statist., Volume 35 (2007) no. 4, pp. 1674-1697 | DOI | MR | Zbl

[6] Chiu, Sung Nok; Stoyan, Dietrich; Kendall, Wilfrid S; Mecke, Joseph Stochastic geometry and its applications, John Wiley & Sons, 2013 | MR | Zbl

[7] Diggle, Peter A Kernel Method for Smoothing Point Process Data, Applied Statistics, Volume 34 (1985) no. 2, pp. 138-147 | Zbl

[8] Elliott, Graham Averaging and the optimal combination of forecasts (2011) (Technical report)

[9] Gaïffas, Stéphane; Lecué, Guillaume Hyper-sparse optimal aggregation, Journal of Machine Learning Research, Volume 12 (2011), pp. 1813-1833 | MR | Zbl

[10] Hansen, Bruce E Least squares model averaging, Econometrica, Volume 75 (2007) no. 4, pp. 1175-1189 | MR | Zbl

[11] Hjort, Nils Lid; Claeskens, Gerda Frequentist model average estimators, Journal of the American Statistical Association, Volume 98 (2003) no. 464, pp. 879-899 | MR | Zbl

[12] Lavancier, Frédéric; Møller, Jesper; Rubak, Ege Determinantal point process models and statistical inference, Journal of the Royal Statistical Society, series B, Volume 77 (2015) no. 4, pp. 853-877 | MR | Zbl

[13] Lavancier, Frédéric; Rochet, Paul A general procedure to combine estimators, Computational Statistics & Data Analysis, Volume 94 (2016), pp. 175-192 | MR | Zbl

[14] Molchanov, Ilya S Statistics of the Boolean model: from the estimation of means to the estimation of distributions, Advances in applied probability (1995), pp. 63-86 | MR | Zbl

[15] Molchanov, Ilya S Statistics of the Boolean Model for Practitioners and Mathematicians, Wiley, Chichester, 1997 | Zbl

[16] Møller, J.; Waagepetersen, R. P. Statistical Inference and Simulation for Spatial Point Processes, Chapman and Hall/CRC, Boca Raton, 2004 | MR | Zbl

[17] R Core Team R: A Language and Environment for Statistical Computing (2016) https://www.R-project.org/

[18] S original by Berwin A. Turlach R port by Andreas Weingessel quadprog: Functions to solve Quadratic Programming Problems. (2013) https://CRAN.R-project.org/package=quadprog (R package version 1.5-5)

[19] Thomas, Marjorie A generalization of Poisson’s binomial limit for use in ecology, Biometrika, Volume 36 (1949) no. 1/2, pp. 18-25 | MR

[20] Timmermann, Allan Forecast combinations, Handbook of Economic Forecasting (Elliott, Graham; Granger, C.W.J; Timmermann, Allan, eds.), North Holland, Amsterdam, 2006, pp. 135-196

[21] Yang, Yuhong Aggregating regression procedures to improve performance, Bernoulli, Volume 10 (2004) no. 1, pp. 25-47 | MR | Zbl