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 几何学 心理学 心理治疗师 经济 业务 会计 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). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Statists. 41, 164– 171. Beale, E. M. L. and Little, R. J. A. (1975). Missing values in multivariate analysis. J. R. Statist. Soc., B, 37, 129– 145. Blight, B. J. N. (1970). Estimation from a censored sample for the exponential family. Biometrika, 57, 389– 395. Brown, M. L. (1974). Identification of the sources of significance in two-way tables. Appl. Statist., 23, 405– 413. Carter, W. H., Jr and Myers, R. H. (1973). Maximum likelihood estimation from linear combinations of discrete probability functions. J. Amer. Statist. Assoc, 68, 203– 206. Ceppellini, R., Siniscalco, M. and Smith, C. A. B. (1955). The estimation of gene frequencies in a random-mating population. Ann. Hum. Genet., 20, 97– 115. Chen, T. and Fienberg, S. (1976). The analysis of contingency tables with incompletely classified data. Biometrics, 32, 133– 144. Corbeil, R. R. and Searle, S. R. (1976). Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics, 18, 31– 38. Day, N. E. (1969). Estimating the components of a mixture of normal distributions. Biometrika, 56, 463– 474. Dempster, A. P. (1972). Covariance selection. Biometrics, 28, 157– 175. Efron, B. (1967). The two-sample problem with censored data. Proc. 5th Berkeley Symposium on Math. Statist. and Prob., 4, 831– 853. Efron, B. and Morris, C. (1975). Data analysis using Stein's estimator and its generalizations. J. Amer. Statist. Assoc, 70, 311– 319. Good, I. J. (1965) The Estimation of Probabilities: An Essay on Modern Bayesian Methods. Cambridge, Mass.: M.I.T. Press. Good, I. J. (1956). On the estimation of small frequencies in contingency tables. J. R. Statist. Soc., B, 18, 113– 124. Grundy, P. M. (1952). The fitting of grouped truncated and grouped censored normal distributions. Biometrika, 39, 252– 259. Haberman, S. J. (1976). Iterative scaling procedures for log-linear models for frequency tables derived by indirect observation. Proc. Amer. Statist. Assoc. (Statist. Comp. Sect. 1975), pp. 45– 50. Hartley, H. O. (1958). Maximum likelihood estimation from incomplete data. Biometrics, 14, 174– 194. Hartley, H. O. and Hocking, R. R. (1971). The analysis of incomplete data. Biometrics, 27, 783– 808. Hartley, H. O. and Rao, J. N. K. (1967). Maximum likelihood estimation for the mixed analysis of variance model. Biometrika, 54, 93– 108. Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. J. Amer. Statist. Assoc, 72, to appear. Hasselblad, V. (1966). Estimation of parameters for a mixture of normal distributions. Technometrics, 8, 431– 444. Hasselblad, V. (1969). Estimation of finite mixtures of distributions from the exponential family. J. Amer. Statist. Assoc, 64, 1459– 1471. Healy, M. and Westmacott, M. (1956). Missing values in experiments analysed on automatic computers. Appl. Statist. 5, 203– 206. Hosmer, D. W. Jr (1973). On the MLE of the parameters of a mixture of two normal distributions when the sample size is small. Comm. Statist., 1, 217– 227. Hosmer, D. W. Jr (1973). A comparison of iterative maximum likelihood estimates of the parameters of a mixture of two normal distributions under three different types of sample. Biometrics, 29, 761– 770. Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73– 101. Irwin, J. O. (1959). On the estimation of the mean of a Poisson distribution with the zero class missing. Biometrics, 15, 324– 326. Irwin, J. O. (1963). The place of mathematics in medical and biological statistics. J. R. Statist. Soc., A, 126, 1– 45. Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183– 202. McKendrick, A. G. (1926). Applications of mathematics to medical problems. Proc. Edin. Math. Soc., 44, 98– 130. Mantel, N. and Greenhouse, S. W. (1967). Note: Equivalence of maximum likelihood and the method of moments in probit analysis. Biometrics, 23, 154– 157. Maritz, J. S. (1970). Empirical Bayes Methods. London: Methuen. Martin, J. K. and McDonald, R. P. (1975). Bayesian estimation in unrestricted factor analysis: A treatment for Heywood cases. Psychometrika, 40, 505– 517. Mosteller, F. and Wallace, D. L. (1964). Inference and Disputed Authorship: The Federalist. Reading, Mass.: Addison-Wesley. Orchard, T. and Woodbury, M. A. (1972). A missing information principle: theory and applications. Proc. 6th Berkeley Symposium on Math. Statist. and Prob. 1, 697– 715. Patterson, H. D. and Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, 58, 545– 554. Raiffa, H. and Schlaifer, R. (1961). Applied Statistical Decision Theory. Cambridge, Mass.: Harvard Business School. Rao, C. R. (1965). 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
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
无情魂幽发布了新的文献求助10
刚刚
天天快乐应助宇航采纳,获得10
刚刚
xuan完成签到,获得积分10
刚刚
刚刚
1秒前
1秒前
3秒前
柔弱山芙完成签到,获得积分10
4秒前
123123完成签到,获得积分10
4秒前
超爱你发布了新的文献求助10
4秒前
大意的觅云完成签到,获得积分10
5秒前
苍耳君发布了新的文献求助10
6秒前
英吉利25发布了新的文献求助10
6秒前
7秒前
cxm666完成签到,获得积分10
7秒前
无情魂幽完成签到,获得积分10
7秒前
鸡蛋布丁完成签到,获得积分10
8秒前
zhongwei2284完成签到,获得积分10
8秒前
慕青应助chsdpolos采纳,获得10
9秒前
欢喜的小海豚完成签到,获得积分10
10秒前
11秒前
飞天小饼发布了新的文献求助10
13秒前
13秒前
时光完成签到,获得积分20
14秒前
平淡豁完成签到,获得积分10
15秒前
15秒前
Mesting发布了新的文献求助10
16秒前
鸡蛋布丁发布了新的文献求助10
16秒前
量子星尘发布了新的文献求助10
17秒前
时光发布了新的文献求助60
17秒前
bianollo发布了新的文献求助20
17秒前
18秒前
黑yan发布了新的文献求助10
18秒前
19秒前
19秒前
LZXS应助srq采纳,获得10
20秒前
20秒前
小二郎应助bai采纳,获得10
22秒前
22秒前
plumageblue完成签到,获得积分10
23秒前
高分求助中
The Mother of All Tableaux Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory 2400
Ophthalmic Equipment Market by Devices(surgical: vitreorentinal,IOLs,OVDs,contact lens,RGP lens,backflush,diagnostic&monitoring:OCT,actorefractor,keratometer,tonometer,ophthalmoscpe,OVD), End User,Buying Criteria-Global Forecast to2029 2000
Optimal Transport: A Comprehensive Introduction to Modeling, Analysis, Simulation, Applications 800
Official Methods of Analysis of AOAC INTERNATIONAL 600
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 588
T/CIET 1202-2025 可吸收再生氧化纤维素止血材料 500
Interpretation of Mass Spectra, Fourth Edition 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3954612
求助须知:如何正确求助?哪些是违规求助? 3500783
关于积分的说明 11100882
捐赠科研通 3231219
什么是DOI,文献DOI怎么找? 1786350
邀请新用户注册赠送积分活动 869980
科研通“疑难数据库(出版商)”最低求助积分说明 801751