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September, 1987 Asymptotically Optimal Cells for a Historgram
Atsuyuki Kogure
Ann. Statist. 15(3): 1023-1030 (September, 1987). DOI: 10.1214/aos/1176350490

Abstract

The purpose of this paper is to examine the properties of the histogram when the cells are allowed to be arbitrary. Given a random sample from an unknown probability density $f$ on $I$, we wish to construct a histogram. Any partition of $I$ can be used as cells. The optimal partition minimizes the mean integrated squared error (MISE) of the histogram from $f$. An expression is found for the infimum of MISE over all partitions. It is proved that the infimum is attained asymptotically by minimizing MISE over a class of partitions of locally equisized cells.

Citation

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Atsuyuki Kogure. "Asymptotically Optimal Cells for a Historgram." Ann. Statist. 15 (3) 1023 - 1030, September, 1987. https://doi.org/10.1214/aos/1176350490

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0631.62049
MathSciNet: MR902243
Digital Object Identifier: 10.1214/aos/1176350490

Subjects:
Primary: 62G05
Secondary: 62E20

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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