A Note on the Aitkin-Rubin Approach to Hypothesis Testing in Mixture Models

In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1987, Vol.49 (3), p.311-314
Main Authors: Quinn, B. G., McLachlan, G. J., Hjort, N. L.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Hypothesis testing
likelihood ratio test
Mathematics
mixture model
Multivariate analysis
Null condition
Null hypothesis
number of components
prior distribution
Probability and statistics
Ratio test
Sciences and techniques of general use
Statistics
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Summary:In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1987.tb01700.x