Applications of Assignment Algorithms to Nonparametric Tests for Homogeneity

• Activity Number: 245
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): David Michael Ruth*+ and Robert Koyak
• Companies: United States Navy and Naval Postgraduate School
• Keywords: nonparametric test ; distribution-free test ; non-bipartite matching ; change point

Abstract

Given a sequence of observations, has a change occurred in the underlying probability distribution with respect to observation order? This problem of detecting "change points" arises in a variety of applications including quality control, health diagnosis, biosurveillance, and image analysis. Detecting change points in high-dimensional settings is challenging, and most change-point methods for multi-dimensional problems rely upon distributional assumptions or the use of observation history to model probability distributions. We present new non-parametric statistical tests for change points based on non-bipartite matching techniques. These tests are capable of detecting changes of quite general nature and require no distributional assumptions. The most powerful among these new tests compares favorably to parametric competitors even when parametric assumptions are met.