Development of inference methods for finite mixture models

本研究项目开发了一种新的有限混合模型推理方法。有限混合模型在应用中非常普遍，但它们的推断是众所周知的困难。具体地说，当检验混合模型中的组件数量时，似然比检验统计量不具有标准的卡方渐近分布。我们发展了一种新的方法来分析有限混合模型的似然函数，并构造了适用于大类模型且具有易于计算的渐近分布的推理程序。此外，我们还通过计算机模拟分析了所提出的方法的有限样本性能。

This research project developed a new method for inference for finite mixture models. Finite mixture models are very popular in applications, but their inference is known to be difficult. Specifically, when one tests for the number of components in a mixture model, the likelihood ratio test statistic does not have the standard chi-square asymptotic distribution. We developed a new approach to analyzing the likelihood function of finite mixture models, and constructed inference procedures that are applicable to a wide class of models and have an easily computable asymptotic distribution. Further, we analyzed the finite sample performance of the proposed procedures by computer simulations.