标题： 混合模型下最大似然估计的一致性 显示英文标题

标题： Consistency of the MLE under mixture models

摘要： 似然基础统计推断在混合模型下的大样本性质受到了统计学家的广泛关注。 尽管非参数最大似然估计的一致性被视为标准结论，但许多研究人员忽略了混合模型所需的精确条件。 即使所研究的混合模型似乎表现良好，不正确的关于一致性的声明也可能导致错误的结论。 例如，在有限正态混合模型下，尽管最近有研究突破，但通常错误地假设普通最大似然估计的一致性。 本文简化了非参数最大似然估计的一致性结果，特别是在有限正态混合模型下的惩罚最大似然估计的情况。 显示英文摘要

摘要： The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consistency of the plain MLE is often erroneously assumed in spite of recent research breakthroughs. This paper streamlines the consistency results for the nonparametric MLE in general, and in particular for the penalized MLE under finite normal mixture models.