Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions

作     者：Coretto, Pietro Hennig, Christian 

作者机构：Univ Salerno Dept Econ & Stat Salerno Italy UCL Dept Stat Sci London WC1E 6BT England 

出 版 物：《JOURNAL OF STATISTICAL PLANNING AND INFERENCE》 (统计规划与统计推断杂志)

年 卷 期：2011年第141卷第1期

页      面：462-473页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Model-based clustering Robustness Identifiability EM-algorithm Hathaway constraints Noise component 

摘      要：Existence and consistency of the Maximum Likelihood estimator of the parameters of heterogeneous mixtures of Gaussian and uniform distributions with known number of components are shown under constraints to prevent the likelihood from degeneration and to ensure identifiability. The EM-algorithm is discussed, and for the special case with a single uniform component a practical scheme to find a good local optimum is proposed. The method is compared theoretically and empirically to the estimation of a Gaussian mixture with noise component as introduced by Banfield and Raftery (1993) to find out whether it is a worthwhile alternative particularly in situations with outliers and points not belonging to the Gaussian components. (C) 2010 Elsevier B.V. All rights reserved.