论文标题
通过小组配合过程估算有限混合模型中的组件数量
Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure
论文作者
论文摘要
在统计数据中，有限混合模型的组件数量（或顺序）的估计是一个持久且具有挑战性的问题。我们提出了群体 - 折线（GSF）程序 - 一种新的惩罚可能性方法，用于同时估算多维有限混合模型中的顺序和混合度量。与使用涉及模型复杂性的标准拟合和比较混合物的方法不同，我们的方法直接惩罚了模型参数的连续函数。更具体地说，给定在阶的保守上限，GSF组和混合组件参数融合了冗余的混合组件参数。对于广泛的有限混合模型，我们表明GSF在估计真实混合物顺序并实现$ n^{ - 1/2} $收敛速率方面是一致的，对于参数估计到polygarogarithmic因素。 GSF是针对R Package oftertFuse中几种单变量和多变量混合模型实施的。它的有限样本性能通过彻底的模拟研究支持，并在两个真实的数据示例中说明了其应用。
Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure -- a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the $n^{-1/2}$ convergence rate for parameter estimation up to polylogarithmic factors. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.
