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Abstract:
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This paper addresses the problems that occur in data analysis due to two types of nonidentifiability in parametric finite mixture models. Although the parameter labels are not identifiable in the strict sense, when the sample size grows large, there is a form of asymptotic identifiability that guarantees the existence of consistent labeling on the parameters. However, the asymptotic theory for maximum likelihood estimation, including asymptotic label identifiability, does not work well when the sample size is not large relative to the separation of the components. There have been very few research studies that analyze the finite sample adequacy of asymptotic methods. In this paper we provide examples that show the breakdown of the asymptotic theory, and then propose a new data-based index that quantifies the degree of identifiability of the labels in finite samples.
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