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.
Publié le : 1987-09-14
Classification:
Histogram,
cells,
partition,
mean integrated squared error,
62G05,
62E20
@article{1176350490,
author = {Kogure, Atsuyuki},
title = {Asymptotically Optimal Cells for a Historgram},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1023-1030},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350490}
}
Kogure, Atsuyuki. Asymptotically Optimal Cells for a Historgram. Ann. Statist., Tome 15 (1987) no. 1, pp. 1023-1030. http://gdmltest.u-ga.fr/item/1176350490/