Selecting the number of bins in a histogram: A decision theoretic approach

Kun He; Glen Meeden

doi:10.1016/s0378-3758(96)00142-5

Selecting the number of bins in a histogram: A decision theoretic approach

Kun He, Glen Meeden

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

In this note we consider the problem of, given a sample, selecting the number of bins in a histogram. A loss function is introduced which reflects the idea that smooth distributions should have fewer bins than rough distributions. A stepwise Bayes rule, based on the Bayesian bootstrap, is found and is shown to be admissible. Some simulation results are presented to show how the rule works in practice.

Original language	English (US)
Pages (from-to)	49-59
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	61
Issue number	1
DOIs	https://doi.org/10.1016/s0378-3758(96)00142-5
State	Published - May 30 1997

Bibliographical note

Funding Information:
* Corresponding author. Research supported in part by NSF Grant SES 9201718. 1 Research supported in part by University of Kansas General Research Fund.

Keywords

Admissibility
Bayesian bootstrap
Histogram
Non-informative Bayes and entropy
Stepwise Bayes

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10.1016/s0378-3758(96)00142-5

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abstract = "In this note we consider the problem of, given a sample, selecting the number of bins in a histogram. A loss function is introduced which reflects the idea that smooth distributions should have fewer bins than rough distributions. A stepwise Bayes rule, based on the Bayesian bootstrap, is found and is shown to be admissible. Some simulation results are presented to show how the rule works in practice.",

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author = "Kun He and Glen Meeden",

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AU - Meeden, Glen

N1 - Funding Information: * Corresponding author. Research supported in part by NSF Grant SES 9201718. 1 Research supported in part by University of Kansas General Research Fund.

PY - 1997/5/30

Y1 - 1997/5/30

N2 - In this note we consider the problem of, given a sample, selecting the number of bins in a histogram. A loss function is introduced which reflects the idea that smooth distributions should have fewer bins than rough distributions. A stepwise Bayes rule, based on the Bayesian bootstrap, is found and is shown to be admissible. Some simulation results are presented to show how the rule works in practice.

AB - In this note we consider the problem of, given a sample, selecting the number of bins in a histogram. A loss function is introduced which reflects the idea that smooth distributions should have fewer bins than rough distributions. A stepwise Bayes rule, based on the Bayesian bootstrap, is found and is shown to be admissible. Some simulation results are presented to show how the rule works in practice.

KW - Admissibility

KW - Bayesian bootstrap

KW - Histogram

KW - Non-informative Bayes and entropy

KW - Stepwise Bayes

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Selecting the number of bins in a histogram: A decision theoretic approach

Abstract

Bibliographical note

Keywords

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