# How many bins should be put in a regular histogram

ESAIM: Probability and Statistics (2006)

- Volume: 10, page 24-45
- ISSN: 1292-8100

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topBirgé, Lucien, and Rozenholc, Yves. "How many bins should be put in a regular histogram." ESAIM: Probability and Statistics 10 (2006): 24-45. <http://eudml.org/doc/249764>.

@article{Birgé2006,

abstract = {
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.
},

author = {Birgé, Lucien, Rozenholc, Yves},

journal = {ESAIM: Probability and Statistics},

keywords = {Regular histograms; density estimation;
penalized maximum likelihood; model selection. ; penalized maximum likelihood; model selection},

language = {eng},

month = {1},

pages = {24-45},

publisher = {EDP Sciences},

title = {How many bins should be put in a regular histogram},

url = {http://eudml.org/doc/249764},

volume = {10},

year = {2006},

}

TY - JOUR

AU - Birgé, Lucien

AU - Rozenholc, Yves

TI - How many bins should be put in a regular histogram

JO - ESAIM: Probability and Statistics

DA - 2006/1//

PB - EDP Sciences

VL - 10

SP - 24

EP - 45

AB -
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.

LA - eng

KW - Regular histograms; density estimation;
penalized maximum likelihood; model selection. ; penalized maximum likelihood; model selection

UR - http://eudml.org/doc/249764

ER -

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