Back To Index Previous Article Next Article Full Text


Statistica Sinica 16(2006), 1299-1312





UNIQUE OPTIMAL PARTITIONS OF DISTRIBUTIONS AND

CONNECTIONS TO HAZARD RATES AND

STOCHASTIC ORDERING


David Mease and Vijayan N. Nair


San Jose State University and University of Michigan


Abstract: Optimal partitioning of a distribution arises in many contexts, including quantization in information theory, piecewise constant approximation of a function, stratified sampling, goodness-of-fit tests, principal points and clustering, and selective assembly in manufacturing. This article studies the behavior of optimal partitions, develops conditions under which the optimal partitioning of a distribution is unique, and establishes connections to hazard rate and likelihood ratio orderings of the distribution. An earlier proof which gives a slightly weaker condition than the sufficient condition in this article is shown to be incorrect by means of a counter-example. Optimal partitioning is compared with some heuristic partitioning strategies that are commonly used in applications and is shown to lead to substantial improvements in efficiency.



Key words and phrases: Likelihood ratio ordering, piecewise constant approximation, quantization, strongly unimodal.

Back To Index Previous Article Next Article Full Text