On derivaton and application of aic as a data-based criterion for histograms |
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Authors: | Taskin Atilgan |
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Institution: | 1. AT&2. T Bell Labor , 600 Mountain Avenue, Room 30J-014, Murray Hill, New Jersey, 07974 |
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Abstract: | In this paper a derivation of the Akaike's Information Criterion (AIC) is presented to select the number of bins of a histogram given only the data, showing that AIC strikes a balance between the “bias” and “variance” of the histogram estimate. Consistency of the criterion is discussed, an asymptotically optimal histogram bin width for the criterion is derived and its relationship to penalized likelihood methods is shown. A formula relating the optimal number of bins for a sample and a sub-sample obtained from it is derived. A number of numerical examples are presented. |
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Keywords: | histograms negative differential entropy penalized likelihood AIC |
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