A variety of statistical problems of optimal grouping, spacing, and stratification are seen to be problems of optimal breakpoint selection for piecewise constant L₂ [0,1] approximation of certain functions. This allows for the development of conditions that insure the existence and uniqueness of solutions, a computational algorithm, and simple approximate solutions. In addition, this approach is shown to provide insight into the relationships between the various problems considered.
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R. L. Eubank (1988) studied this question.
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