1977 MaximumLikelihoodFromIncompleteData

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Subject Headings: EM Algorithm, Maximum Likelihood Estimation Algorithm, Highly-Cited Paper.


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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.


  • BARGMANRN., (1957). A study of independence and dependence in multivariate normal analysis. Mimeo Series No. 186, University of North Carolina.
  • BATSCHELEET., (1960). 'Uber eine Kontingenztagel mit fehlenden Daten. Biometr. Zeitschr., 2, 236-243.
  • BISHOPY, . M. M., FIENBERGS., E. and HOLLANDP,. W. (1975). Discrete Multivariate Analysis: Theory and Practice. Cambridge, Mass. : M.I.T. Press.
  • DEMPSTERA,. P. and MONAJEMAI,. (1976). An algorithmic approach to estimating variances. Research Report S-42, Dept of Statistics, Harvard University.
  • DRAPERN, . R. and GUTTMANI., (1968). Some Bayesian stratified two-phase sampling results. Biometrika, 55, 131-140 and 587-588.
  • EDWARDAS,. W. F. (1970). Estimation of the branch points of a branching diffusion process (with Discussion). J. R. Statist. Soc. B, 32, 155-174.
  • FEDOROVV,. V. (1972). Theory of Optimal Experiments (E. M. Klimko and W. J. Studden, eds and translators). New York: Academic Press.
  • FELLMANJ., (1974). On the allocation of linear observations. Commentationes Phys.-Math., 44, Nos. 2-3.
  • FISHERR, . A. (1925). Theory of statistical estimation. Proceedings of Camb. Phil. Soc., 22, 700-725.
  • GEPPERT, M. P. (1961). Erwartungstreue plausibelste Schutzen aus dreieckig gestutzen Kontingenstafeln. Biometr. Zeitschr., 3, 54-67.
  • GOODMANL., A. (1968). The analysis of cross-classified data. Independence, quasi-independence and interaction in contingency tables with or without missing entries. J. Amer. Statist. Ass., 63, 1091-1131.
  • GOODMANL., A. (1974). Exploratory latent-structure analysis using both identifiable and unidentifiable models. Biometrika, 61,215-23 1.
  • GUTTMANI., (1971). A remark on the optimal regression designs with previous observations of Covey-Crump and Silvey. Biometrika, 58, 683-685.
  • HABERMASN., J. (1971). Tables based on imperfect observation. Invited paper at the 1971 ENAR meeting, Pennsylvania State University.
  • HABERMASN., J. (1974). Loglinear models for frequency tables derived by indirect observation: maximum likelihood equations. Ann. Statist., 2, 911-924.
  • HEMMERLWE,. J. (1974). Nonorthogonal analysis of variance using iterative improvement and balanced residuals. J. Amer. Statist. Ass., 69, 772-778.
  • HEMMERLWE,. J. and HARTLEYH, . 0. (1973). Computing maximum likelihood estimates for the mixed A.O.V. model using the W transformation. Technometrics, 15, 819-831.
  • HEMMERLWE., J. and LORENSJ,. 0. (1976). Improved algorithm for the W-transform in variance component estimation. Technometrics, 18, 207-212.
  • Howe, W. G. (1955). Some contributions to factor analysis. Report ORNL 1919, Oak Ridge National Laboratory.
  • LAIRDN, . M. (1975). Log-linear models with random parameters. Ph.D. Thesis, Harvard University.
  • LAIRDN, . M. (1976). Nonparametric maximum-likelihood estimation of a distribution function with mixtures of distributions. Technical Report S-47, NS-338, Dept of Statistics, Harvard University.
  • LAWLEYD,. N. and MAXWELLA,. E. (1971). Factor Analysis as a Statistical Method (2nd edn). London: Butterworth.
  • LITTLE, R. J. A. (1974). Missing values in multivariate statistical analysis. Ph.D. Thesis, University of London.
  • MCCLACHLAGN., J. (1975). Iterative reclassification procedure for constructing an asymptotically optimal rule of allocation in discriminant analysis. J. Amer. Statist. Ass., 70, 365-369.
  • MORGANB,. J. T. and TITTERINGTODN., M. (1977). A comparison of iterative methods for obtaining maximum-likelihood estimates in contingency tables with a missing diagonal. Biometrika, 64, (in press).
  • PEARCES,. C. (1965). Biological Statistics: an Introduction. New York: McGraw-Hill.
  • PEARCES., C. and JEFFERSJ., N. R. (1971). Block designs and missing data. J.R. Statist. Soc. B, 33,131-136.
  • PETERSOAN., V. (1975). Nonparametric estimation in the competing risks problem. Ph.D. Thesis, Stanford University.
  • PREECED, . A. (1971). Iterative procedures for missing values in experiments. Technometrics, 13, 743-753.
  • RAO,C. R. (1955). Estimation and tests of significance in factor analysis. Psychometrika, 20, 93.
  • RUBIN, D. R. (1972). A non-iterative algorithm for least squares estimation of missing values in any analysis of variance design. Appl. Statist., 21, 136-141. 38 Discussion on the Paper by Professor Dempster et al. [No. 1,
  • SILVEYS, . D., TITTERINGTODN., M. and TORSNEYB,. (1976). An algorithm for D-optimal designs on a h i t e space. Report available from the authors.
  • SMITH, C. A. B. (1969). Biomathematics, Vol. 2. London: Griffin.
  • SNEDECORG,. W. and COCHRANW, . G. (1967). Statistical Methods, 6th edn. Ames, Iowa: Iowa State University Press.
  • THOMPSOEN., A. (1975). Human Evolutionary Trees. Cambridge: Cambridge University Press.
  • TsIAns, A. (1975). A nonidentifiability aspect of the problem of competing risks. Proceedings of Nut. Acad. Sci. USA, 71, 20-22.
  • TUKEY, J. W. (1962). The future of data analysis. Ann. Math. Statist., 33, 1-67.
  • TURNBULBL., W. (1976). The empirical distribution function with arbitrarily grouped censored and truncated data. J. R. Statist. Soc. B, 38, 290-295.
  • TURNBULBL., W. and WEISSL, . (1976). A likelihood ratio statistic for testing goodness of fit with randomly censored data. Technical Report No. 307, School of Operations Research, Cornell University.,

 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
1977 MaximumLikelihoodFromIncompleteDataArthur P. Dempster
Nan Laird
Donald Rubin
Maximum Likelihood from Incomplete Data via the EM AlgorithmJournal of the Royal Statistical Societyhttp://www.jstor.org/pss/29848751977