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首页> 外文期刊>Journal of computational and graphical statistics: A joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America >A Functional EM Algorithm for Mixing Density Estimation via Nonparametric Penalized Likelihood Maximization
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A Functional EM Algorithm for Mixing Density Estimation via Nonparametric Penalized Likelihood Maximization

机译：基于非参数惩罚似然最大化的混合密度估计的函数EM算法

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摘要

When the true mixing density is known to be continuous, the maximum likelihood estimate of the mixing density does not provide a satisfying answer due to its degeneracy. Estimation of mixing densities is a well-known ill-posed indirect problem. In this article, we propose to estimate the mixing density by maximizing a penalized likelihood and call the resulting estimate the nonparametric maximum penalized likelihood estimate (NPMPLE). Using theory and methods from the Calculus of variations and differential equations, a new functional EM algorithm is derived for computing the NPMPLE of the mixing density. In the algorithm, maximizers in M-steps are found by solving all ordinary differential equation with boundary conditions numerically. Simulation studies show the algorithm outperforms other existing methods such as the popular EMS algorithm. Some theoretical properties of the NPMPLE and the algorithm are also discussed. Computer code used in this article is available online.
机译：当已知真实的混合密度是连续的时，由于混合密度的简并性，混合密度的最大似然估计不能提供令人满意的答案。混合密度的估计是众所周知的不适定间接问题。在本文中，我们建议通过最大化惩罚可能性来估计混合密度，并将得到的估计值称为非参数最大惩罚可能性估计值（NPMPLE）。利用变分和微分方程微积分的理论和方法，推导了一种新的函数EM算法，用于计算混合密度的NPMPLE。在该算法中，通过数值求解所有带边界条件的常微分方程，可以找到M步的最大化子。仿真研究表明，该算法优于其他现有方法，例如流行的EMS算法。还讨论了NPMPLE和算法的一些理论特性。本文中使用的计算机代码可在线获得。

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