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Article
Unique Optimal Partitions of Distributions and Connections to Hazard Rates and Stochastic Ordering
Statistica Sinica (2006)
  • David Mease, San Jose State University
  • V. N. Nair, University of Michigan - Ann Arbor
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.

Keywords
  • Likelihood ratio ordering,
  • piecewise constant approximation,
  • quantization,
  • strongly unimodal
Publication Date
2006
Citation Information
David Mease and V. N. Nair. "Unique Optimal Partitions of Distributions and Connections to Hazard Rates and Stochastic Ordering" Statistica Sinica Vol. 16 (2006)
Available at: http://works.bepress.com/david_mease/7/