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Consistency and identifiability revisited. (English) Zbl 1049.62003

Summary: We provide a general framework to review the well-known concept of identifiability and give a formal proof that this is implied by the existence of a consistent estimator. We apply these ideas to the predictive recursion algorithm for finite mixtures to conclude that identifiability is actually equivalent to consistency.

MSC:

62A01 Foundations and philosophical topics in statistics
62F12 Asymptotic properties of parametric estimators
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