Robust estimation in the normal mixture model
Robust estimation in the normal mixture model
复制标题
DOI：
10.1016/j.jspi.2005.03.008
复制
发表时间：
2006-11-01
影响因子：
0.9
通讯作者：
Eguchi, Shinto
中科院分区：
文献类型：
--
作者：
Fujisawa, Hironori;Eguchi, Shinto
本文主要研究方差不等的正态混合模型的推断问题。该模型的一个特点是密度形状的灵活性，但它的灵活性导致了似然函数的无界性和极大似然估计对离群值的过度敏感性。Basu等人[1998，Biometrika 85，549-559]中提出的修改的似然方法可以克服这些缺点。证明了在混合比例较弱的条件下，修正后的似然函数上有界，且所得估计对离群值是鲁棒的。基于鲁棒模型选择准则和交叉验证，研究了鲁棒性与效率之间的关系，提出了一种自适应选择修正似然模型调整参数的方法。还构造了一个类EM算法。数值研究，以评估性能。稳健的方法被应用于单个核苷酸多态性分型，用于离群值检测和聚类的目的。(c)2005 Elsevier B. V.保留所有权利。
This paper focuses on the inference of the normal mixture model with unequal variances. A feature of the model is flexibility of density shape, but its flexibility causes the unboundedness of the likelihood function and excessive sensitivity of the maximum likelihood estimator to outliers. A modified likelihood approach suggested in Basu et al. [1998, Biometrika 85, 549-559] can overcome these drawbacks. It is shown that the modified likelihood function is bounded above under a mild condition on mixing proportions and the resultant estimator is robust to outliers. A relationship between robustness and efficiency is investigated and an adaptive method for selecting the tuning parameter of the modified likelihood is suggested, based on the robust model selection criterion and the cross-validation. An EM-like algorithm is also constructed. Numerical studies are presented to evaluate the performance. The robust method is applied to single nuleotide polymorphism typing for the purpose of outlier detection and clustering. (c) 2005 Elsevier B.V. All rights reserved.