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Abstract:
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Consider estimators that are ratios of two sums, each of n terms. Examples include proportions, regression and partial regression coefficients, and Mantel-Haenszel odds ratio estimators. Such estimators share a diagnostic plot, the N-D plot, which plots the cumulative sums of the numerator terms against their respective denominator sums. The application of N-D plots depends critically on the order in which the terms are sorted and summed. This work develops the distributional properties and generalizes N-D plots to multiply-indexed sort orders. We illustrate with a diverse range of applications: empirical segmentations over a continuous scale, goodness-of-fit assessment for black box and layered models, and the concurrent validity of newly proposed metrics.
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