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February, 1995 Optimal Rate of Convergence for Finite Mixture Models
Jiahua Chen
Ann. Statist. 23(1): 221-233 (February, 1995). DOI: 10.1214/aos/1176324464


In finite mixture models, we establish the best possible rate of convergence for estimating the mixing distribution. We find that the key for estimating the mixing distribution is the knowledge of the number of components in the mixture. While a $\sqrt n$-consistent rate is achievable when the exact number of components is known, the best possible rate is only $n^{-1/4}$ when it is unknown. Under a strong identifiability condition, it is shown that this rate is reached by some minimum distance estimators. Most commonly used models are found to satisfy the strong identifiability condition.


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Jiahua Chen. "Optimal Rate of Convergence for Finite Mixture Models." Ann. Statist. 23 (1) 221 - 233, February, 1995.


Published: February, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0821.62023
MathSciNet: MR1331665
Digital Object Identifier: 10.1214/aos/1176324464

Primary: 62G05
Secondary: 62G20

Keywords: local asymptotic normality , maximum likelihood estimate , minimum distance , mixing distribution , mixture model , rate of convergence , strong identifiability

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 1 • February, 1995
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