An indifference zone approach to testing for a two-component normal mixture
by
Kerrie Mengersen
The University of Newcastle
Coauthors: Michele Haynes

Traditional ranking and selection methods have been concerned with the degree of separation between populations with respect to some parameter of interest. An approach considered here directly models the data through a normal mixture distribution and applies a test for the number of components in the mixture to determine the rank and allocation of populations to an unknown number of groups. Inference concerning the size of the difference between groups of populations is then made in terms of the distributional distance between normal mixture distributions with K and (K-1) components, respectively. We focus on a test for a two-component normal mixture model by assessing the “closeness” of the mixture to a normal distribution, relative to some indifference zone defined through an L2 metric which is applicable in both Bayesian and frequentist settings and allows easy generalisation to more than two components. This extends an earlier analogous test based on the Kullback-Leibler distributional distance. Consideration is also given to model selection using predictive densities under a Bayesian approach.

Date received: November 4, 2001