The optimal construction of a histogram is a fundamental task in data analysis. Many rules of thumb are available to get started. Some use the normal density as a reference distribution. Scott's rule is of that class, using as the measure of discrepancy the mean integrated squared error. This article discusses the origin and formulation of this formula, as well as comparisons with some other formulae and their relative performance.
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David W. Scott (2010) studied this question.
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