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DOI : 10.1051/ps:2006001

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ESAIM: Probability and Statistics 10 (2006) 24-45

HOW MANY BINS SHOULD BE PUT IN A REGULAR HISTOGRAM

Lucien Birgé 1, Yves Rozenholc 2

(02/2006)

Given an n-sample from some unknown density f on [0,1], it is easy to construct an histogram of the data based on some given partition of [0,1], but not so much is known about an optimal choice of the partition, especially when the data set is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of f. Our purpose in this paper is to give an automatic, easy to program and efficient method to choose the number of bins of the partition from the data. It is based on bounds on the risk of penalized maximum likelihood estimators due to Castellan and heavy simulations which allowed us to optimize the form of the penalty function. These simulations show that the method works quite well for sample sizes as small as 25.

1 :	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
2 :	Mathématiques appliquées Paris 5 (MAP5)
	CNRS : UMR8145 – Université Paris V - Paris Descartes

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Mathématiques/Statistiques Statistiques/Théorie Statistiques/Applications

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Contributeur : Yves Rozenholc <>

Soumis le : Mercredi 27 Juin 2012, 01:01:32

Dernière modification le : Mercredi 27 Juin 2012, 08:46:22