Abstract
Scott, Freedman, and Diaconis derived expressions for optimal interval widths in fixed-interval univariate histograms and Terrell and Scott obtained corresponding results for variable-interval univariate histograms. The present paper considers the more general problem of optimal fixed and variable cell dimensions in several varieties of bivariate histograms. Optimal cell dimensions are derived, theoretically optimal histograms are constructed, and simulation studies are performed.
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