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Maximum Likelihood from Incomplete Data Via the EM Algorithm

超参数 期望最大化算法 单调多边形 缺少数据 概括性 计算机科学 算法 最大似然 趋同(经济学) 限制最大似然 差异(会计) 最大似然序列估计 应用数学 数学 统计 心理学 业务 几何学 会计 经济 心理治疗师 经济增长
作者
A. P. Dempster,Nan M. Laird,Donald B. Rubin
出处
期刊:Journal of the royal statistical society series b-methodological [Wiley]
卷期号:39 (1): 1-22 被引量:20895
标识
DOI:10.1111/j.2517-6161.1977.tb01600.x
摘要

Journal of the Royal Statistical Society: Series B (Methodological)Volume 39, Issue 1 p. 1-22 ArticleFree Access Maximum Likelihood from Incomplete Data Via the EM Algorithm A. P. Dempster, A. P. Dempster Harvard University and Educational Testing ServiceSearch for more papers by this authorN. M. Laird, N. M. Laird Harvard University and Educational Testing ServiceSearch for more papers by this authorD. B. Rubin, D. B. Rubin Harvard University and Educational Testing ServiceSearch for more papers by this author A. P. Dempster, A. P. Dempster Harvard University and Educational Testing ServiceSearch for more papers by this authorN. M. Laird, N. M. Laird Harvard University and Educational Testing ServiceSearch for more papers by this authorD. B. Rubin, D. B. Rubin Harvard University and Educational Testing ServiceSearch for more papers by this author First published: 1977 https://doi.org/10.1111/j.2517-6161.1977.tb01600.xCitations: 8,788AboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis. References Andrews, D. F., Bickel, P. J., Hampel, F., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1972). Robust Estimates of Location. Princeton, N.J.: Princeton University Press. Baum, L. E. (1971). An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. In Inequalities, III: Proceedings of a Symposium. ( Qved Shisha ed.). New York: Academic Press. Baum, L. E. and Eagon, J. A. (1967). An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology. Bull. Amer. Math. Soc., 73, 360– 363. Baum, L. E., Petrie, T., Soules, G. and Weiss, N. (1970). 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Linear Statistical Inference and its Applications. New York: Wiley. Rubin, D. B. (1974). Characterizing the estimation of parameters in incomplete-data problems. J. Amer. Statist. Assoc, 69, 467– 474. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581– 592. Sundberg, R. (1974). Maximum likelihood theory for incomplete data from an exponential family. Scand. J. Statist., 1, 49– 58. Sundberg, R. (1976). An iterative method for solution of the likelihood equations for incomplete data from exponential families. Comm. Statist–Simula. Computa., B5(1), 55– 64. Turnbull, B. W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Assoc, 69, 169– 173. Turnbull, B. W. (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Statist. Soc., B, 38, 290– 295. Wolfe, J. H. (1970). Pattern clustering by multivariate mixture analysis. Multivariate Behavioral Research, 5, 329– 350. Woodbury, M. A. (1971). Discussion of paper by Hartley and Hocking. Biometrics, 27, 808– 817. Citing Literature Volume39, Issue11977Pages 1-22 This article also appears in:Discussion Papers ReferencesRelatedInformation
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