A linearization procedure and a VDM/ECM algorithm for penalized and constrained nonparametric maximum likelihood estimation for mixture models

作     者：Wang, Ji-Ping 

作者机构：Northwestern Univ Dept Stat Evanston IL 60208 USA 

出 版 物：《COMPUTATIONAL STATISTICS & DATA ANALYSIS》 (计算统计学与数据分析)

年 卷 期：2007年第51卷第6期

页      面：2946-2957页

核心收录：

学科分类：08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：mixture models nonparametric maximum likelihood computing algorithm penalized NPMLE constrained NPMLE VDM/ECM 

摘      要：Suppose independent observations X-i, i = 1,..., n are observed from a mixture model f(x;Q) equivalent to integral f (x;lambda) d Q (lambda), where lambda is a scalar and Q(lambda) is a nondegenerate distribution with an unspecified form. We consider to estimate Q(lambda) by nonparametric maximum likelihood (NPML) method under two scenarios: (1) the likelihood is penalized by a functional g(Q);and (2)Q is under a constraint g(Q) = g(0). We propose a simple and reliable algorithm termed VDM/ECM for Q-estimation when the likelihood is penalized by a linear functional. We show this algorithm can be applied to a more general situation where the penalty is not linear, but a function of linear functionals by a linearization procedure. The constrained NPMLE can be found by penalizing the quadratic distance vertical bar g(Q) - g(0)vertical bar(2) under a large penalty factor gamma 0 using this algorithm. The algorithm is illustrated with two real data sets. (c) 2006 Elsevier B.V. All rights reserved.