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Averaged shifted histogram

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Abstract The averaged shifted histogram or ASH is a nonparametric probability density estimator derived from a collection of histograms. The ASH enjoys several advantages compared with a single histogram: better visual interpretation, better approximation, and nearly the same computational efficiency. The ASH provides a bridge between the histogram and advanced kernel methods; moreover, the ASH provides a method of choice for kernel implementation. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation

Three histogram estimates of Sosa's home run distances with bin widths of 12.5, 25, and 50 feet (left to right).

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Comparison of Sosa's (gray) and McGwire's (red hatched) home runs; ASH (m = 32).

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Comparison of Sosa's home (gray) and away (red hatched) home runs with a histogram and an ASH (m = 32).

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Triweight ASH estimates with m = 1, 2, 4, …, 32.

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Triangle ASH estimates of the Sosa data with .

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Three histograms of the Sosa home run data using the same bin width of 25 feet, but different bin origins.

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Statistical and Graphical Methods of Data Analysis > Density Estimation

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