论文标题
von Mises-fisher分布的混合物的惩罚最大似然估计器
Penalized Maximum Likelihood Estimator for Mixture of von Mises-Fisher Distributions
论文作者
论文摘要
von mises-fisher分布是描述定向数据的最广泛使用的概率分布之一。冯·米塞斯·菲什（Von Mises-Fisher）分布的有限混合物发现了许多应用。但是，von mises-fisher分布的有限混合物的可能性函数是无限的，因此最大似然估计的定义不当。为了解决似然堕落的问题，我们考虑了一种惩罚最大似然方法，从而纳入了惩罚功能。我们证明了由此产生的估计器的强大一致性。开发了惩罚似然函数的期望最大化算法，并进行了模拟研究以检查其性能。
The von Mises-Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises-Fisher distributions have found numerous applications. However, the likelihood function for the finite mixture of von Mises-Fisher distributions is unbounded and consequently the maximum likelihood estimation is not well defined. To address the problem of likelihood degeneracy, we consider a penalized maximum likelihood approach whereby a penalty function is incorporated. We prove strong consistency of the resulting estimator. An Expectation-Maximization algorithm for the penalized likelihood function is developed and simulation studies are performed to examine its performance.
