Fast Algorithms for Estimating Mixture Parameters

本研究关注的是快速算法的发展，用于估计在许多统计模型中出现的与有限混合密度相关的混合参数。估计参数通常是困难的，而且不希望耗费时间。本研究的中心目标是确定快速迭代程序，以近似这些参数的最大似然估计。提出了两大类迭代方法。第一类由特殊的拟牛顿方法组成。它们被设计成利用对数似然函数的特殊结构。第二类是对流行的EM算法进行修改。它们旨在展示加速收敛，同时保留EM算法的许多优点。

This study is concerned with the development of fast algorithms for estimating mixture parameters associated with finite mixture densities that arise in many statistical models. Estimating the parameters is often difficult and undesirably time- consuming. The central objective of this research is to determine fast iterative procedures for approximating maximum- likelihood estimates of these parameters. Two broad types of iterative methods are proposed. The first type consists of special quasi-Newton methods. They are designed to take advantage of the special structure of the log-likelihood function. The second type consists of modifications of the popular EM algorithm. They are intended to exhibit accelerated convergence while preserving many of the advantages of the EM algorithm.