An optimal variable cell histogram

1 January 1988

journal article
research article
Published by Taylor & Francis in Communications in Statistics - Theory and Methods

Vol. 17 (5) , 1401-1422
https://doi.org/10.1080/03610928808829688

Abstract

A simple procedure for specifying a histogram with variable cell sizes is proposed. The procedure chooses a set of cutpoints that maximizes a criterion function based on the sample spacings:Under some conditions, this estimated set of cutpoints is shown to converge in probability to the theoretical set of cutpoints for the histogram estimate that minimizes the Hellingerdistance to the underlying density. An algorithm for finding the set of cutpoints that numerically maximizes the criterion function is presented along with an example. Performance for finite sample sizes is evaluated by simulations.

Keywords

This publication has 3 references indexed in Scilit:

Asymptotically Optimal Cells for a Historgram
The Annals of Statistics, 1987
On the histogram as a density estimator:L 2 theory
Probability Theory and Related Fields, 1981
Spacings
Journal of the Royal Statistical Society Series B: Statistical Methodology, 1965