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Wikipedia's nice article on the histogram contains the following sentence:

"Using wider bins where the density of the underlying data points is low reduces noise due to sampling randomness; using narrower bins where the density is high (so the signal drowns the noise) gives greater precision to the density estimation."

without an actual source which can then be cited.

Does someone know if there is a specific paper in the literature that mentions this point to some effect?

Googling keywords has not turned up anything in this regard.

compbiostats
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  • Does this thread address your question? https://stats.stackexchange.com/questions/798/calculating-optimal-number-of-bins-in-a-histogram/862#862 – mkt Oct 09 '19 at 15:32
  • @mkt I was actually looking for a specific reference. But the post you linked to does contain some. I guess the quote I gave above can just be taken as a "given". – compbiostats Oct 09 '19 at 16:10
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    If it covers it, we can close this as a duplicate. If it doesn't, could you edit your question to highlight what is not covered? – mkt Oct 09 '19 at 16:14
  • The variance of each bin is proportional to the number of results it represents: this basic fact about variances immediately implies the Wikipedia statement. – whuber Oct 09 '19 at 19:52
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    @mkt I did find some literature in the post you mention. whuber's comment is also satisfactory. Thanks. – compbiostats Oct 10 '19 at 00:10
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    [This post](https://stats.stackexchange.com/questions/339194/can-the-bin-size-in-a-histogram-be-thought-of-as-a-regularity-constraint/339453#339453) contains a reference that addresses your question (Scott 1979). – user20160 Oct 10 '19 at 00:18
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    Just a small note in cases where people want *something* to cite and all they have is a post here: it's possible to cite a post (though not every journal will be happy with that, some may be fine with it); there's even a grey "cite" link at the bottom of each post (just to the left of the grey "edit" link) which can generate a citation in a couple of standard ways. Try it. – Glen_b Oct 10 '19 at 00:39

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