Please use this identifier to cite or link to this item:
|Title: ||Asymptotic methods for tests of homogeneity for finite mixture models|
|Authors: ||Stewart, Michael Ian|
|Keywords: ||Mixture models;asymptotic distribution;test of homogeneity;extremes of Gaussian processes;empirical processes|
|Issue Date: ||2002|
|Publisher: ||University of Sydney. Mathematics and Statistics|
|Abstract: ||We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.|
|Rights and Permissions: ||Copyright Stewart, Michael Ian;http://www.library.usyd.edu.au/copyright.html|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
This work is protected by Copyright. All rights reserved. Access to this work is provided for the purposes of personal research and study. Except where permitted under the Copyright Act 1968, this work must not be copied or communicated to others without the express permission of the copyright owner. Use the persistent URI in this record to enable others to access this work.
Items in Sydney eScholarship Repository are protected by copyright, with all rights reserved, unless otherwise indicated.