Hall, Peter; Stewart, Michael
In a likelihood-ratio test for a two-component Normal location mixture, the natural parametrisation degenerates to non-uniqueness under the null hypothesis. One consequence of this ambiguity is that the limiting distribution of the likelihood-ratio statistic is quite irregular, being of extreme-value type rather than chi-squared. Another irregular feature is that the likelihood-ratio statistic diverges to infinity, and so limit theory is nonstandard in this respect as well. These results, in a...[Show more]
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