OPTIMAL RATE OF CONVERGENCE FOR FINITE MIXTURE-MODELS
成果类型：
Article
署名作者：
CHEN, JH
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176324464
发表日期：
1995
页码：
221-233
关键词：
摘要：
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 root 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.