An optimal variable cell histogram

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:

• density estimation
• Hellinger distance
• histogram