Algorithme EM : théorie et application au modèle mixte
Journal de la Société française de statistique, Tome 143 (2002) no. 3-4, pp. 57-109.
@article{JSFS_2002__143_3-4_57_0,
     author = {Foulley, Jean-Louis},
     title = {Algorithme {EM} : th\'eorie et application au mod\`ele mixte},
     journal = {Journal de la Soci\'et\'e fran\c{c}aise de statistique},
     pages = {57--109},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {143},
     number = {3-4},
     year = {2002},
     language = {fr},
     url = {http://archive.numdam.org/item/JSFS_2002__143_3-4_57_0/}
}
TY  - JOUR
AU  - Foulley, Jean-Louis
TI  - Algorithme EM : théorie et application au modèle mixte
JO  - Journal de la Société française de statistique
PY  - 2002
SP  - 57
EP  - 109
VL  - 143
IS  - 3-4
PB  - Société française de statistique
UR  - http://archive.numdam.org/item/JSFS_2002__143_3-4_57_0/
LA  - fr
ID  - JSFS_2002__143_3-4_57_0
ER  - 
%0 Journal Article
%A Foulley, Jean-Louis
%T Algorithme EM : théorie et application au modèle mixte
%J Journal de la Société française de statistique
%D 2002
%P 57-109
%V 143
%N 3-4
%I Société française de statistique
%U http://archive.numdam.org/item/JSFS_2002__143_3-4_57_0/
%G fr
%F JSFS_2002__143_3-4_57_0
Foulley, Jean-Louis. Algorithme EM : théorie et application au modèle mixte. Journal de la Société française de statistique, Tome 143 (2002) no. 3-4, pp. 57-109. http://archive.numdam.org/item/JSFS_2002__143_3-4_57_0/

Anderson T.W. (1984), An introduction to multivariate analysis, J Wiley and Sons, New York. | MR

Anderson D.A., Aitkin M. (1985), Variance components models with binary response : interviewer probability, Journal of the Royal Statistical Society B, 47, 203-210. | MR

Aitkin M. (1987), Modelling variance heterogeneity in normal regression using GLIM, Applied Statistics, 36, 332-339.

Booth J.G., Hobert J.P. (1999), Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society B, 61,265-285. | Zbl

Boyles R.A. (1983), On the convergence of the EM algorithm, Journal of the Royal Statistical Society B, 45, 47-50. | MR | Zbl

Celeux G., Diebolt J. (1985), The SEM algorithm : a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem, Computational Statistics Quaterly, 2, 73-82.

Celeux G., Diebolt J. (1992), A Stochastic Approximation Type EM Algorithm for the Mixture Problem, Stochastics and Stochastics Reports, 41, 119-134. | MR | Zbl

Celeux G., Govaert G. (1992), A classification algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, 315-322. | Zbl

Celeux G., Chauveau D., Diebolt J. (1996), Some stochastic versions of the EM algorithm. Journal of Statistical Computation and Simulation, 55, 287-314. | Zbl

Delmas C., Foulley J.L., Robert-Granié C. (2002), Further insights into tests of variance components and model selection, Proceedings of the 7th World Congress of Genetics applied to Livestock Production, Montpellier, France, 19-23 August 2002.

Delyon B., Lavielle M., Moulines E. (1999), Convergence of a stochastic approximation version of the EM algorithm, Annals of Statistics, 27, 94-128. | MR | Zbl

Dempster A., Laird N., Rubin R. (1977), Maximum likelihood estimation from incomplete data via the EM algorithm, Journal of the Royal Statistical Society B, 39,1-38. | MR | Zbl

Efron B. (1977), Discussion on maximum likelihood from incomplete data via the EM algorithm (by Dempster A., Laird N., Rubin R.), Journal of the Royal Statistical Society B, 39, 1-38. | MR | Zbl

Fisher R.A. (1925), Theory of statistical estimation, Proceedings of the Cambridge Philosophical Society, 22, 700-725. | JFM

Foulley J.L. (1993), A simple argument showing how to derive restricted maximum likelihood, Journal of Dairy Science, 76, 2320-2324.

Foulley J.L. (1997), ECM approaches to heteroskedastic mixed models with constant variance ratios. Genetics Selection Evolution, 29, 297-318.

Foulley J.L., Im S., Gianola D., Hoeschele I. (1987), Empirical Bayes estimation of parameters for n polygenic binary traits, Genetics Selection Evolution, 19, 127-224.

Foulley J.L., San Cristobal M., Gianola D., Im S. (1992), Marginal likelihood and Bayesian approaches to the analysis of heterogeneous residual variances in mixed linear Gaussian models, Computational Statistics and Data Analysis, 13, 291-305. | Zbl

Foulley J.L., Quaas R.L. (1995), Heterogeneous variances in Gaussian linear mixed models, Genetics Selection Evolution, 27, 211-228.

Foulley J.L., Quaas R.L., Thaon D'Arnoldi C. (1998), A link function approach to heterogeneous variance components, Genetics Selection Evolution, 30, 27-43.

Foulley J.L., Van Dyk D.A. (2000), The PX EM algorithm for fast fitting of Henderson's mixed model, Genetics Selection Evolution, 32, 143-163.

Foulley J.L., Jaffrezic F., Robert-Granié C. (2000), EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis, Genetics Selection Evolution, 32, 129-141.

Foulley J.L., Delmas C., Robert-Granié C. (2002), Méthodes du maximum de vraisemblance en modèle linéaire mixte, Journal de la Société Française de Statistique, 143, 1-2, 5-52.

Grimaud A., Huet S., Monod H., Jenczewski E., Eber F. (2002), Mélange de modèles mixtes : application à l'analyse des appariements de chromosomes chez des haploïdes de colza, Journal de la Société Française de Statistique, 143, 1-2, 147-153.

Hartley H.O., Rao J.N.K. (1967), Maximum likelihood estimation for the mixed analysis of variance model, Biometrika, 54, 93-108. | MR | Zbl

Harville D.A. (1974), Bayesian inference for variance components using only error contrasts, Biometrika, 61, 383-385. | MR | Zbl

Harville D.A. (1977), Maximum likelihood approaches to variance component estimation and to related problems, Journal of the American Statistical Association, 72, 320-340. | MR | Zbl

Henderson C.R. (1973), Sire evaluation and genetic trends, In : Proceedings of the animal breeding and genetics symposium in honor of Dr J Lush. American Society Animal Science-American Dairy Science Association, 10-41, Champaign, IL.

Henderson C.R. (1984), Applications of linear models in animal breeding, University of Guelph, Guelph, 1984.

Kuhn E., Lavielle M. (2002), Coupling a stochastic approximation version of EM with a MCMC procedure, Rapport technique, Université Paris Sud, 15 pages.

Laird N.M. (1982), The computation of estimates of variance components using the EM algorithm, Journal of Statistical Computation and Simulation, 14, 295-303. | MR | Zbl

Laird N.M., Ware J.H. (1982), Random effects models for longitudinal data, Biometrics, 38 963-974. | Zbl

Laird N.M., Lange N., Stram D. (1987), Maximum likelihood computations with repeated measures : Application of the EM algorithm. Journal of the American Statistical Association, 82, 97-105. | MR | Zbl

Lange K. (1995), A gradient algorithm locally equivalent to the EM algorithm, Journal of the Royal Statistical Society B, 57, 425-437. | MR | Zbl

Leonard T. (1975), A Bayesian approach to the linear model with unequal variances, Technometrics, 17, 95-102. | MR | Zbl

Leonard T., Hsu Jsj. (1999), Bayesian methods, an analysis for statisticians and interdisciplinary researchers, Cambridge University Press, Cambridge, UK. | MR | Zbl

Liang K.Y., Zeger S.L. (1986), Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. | MR | Zbl

Liao J.G., Lipsitz S.R. (2002) A type of restricted maximum likelihood estimator of variance components in generalized linear mixed models, Biometrika, 89, 401-409. | MR | Zbl

Lindley D.V., Smith A.F.M. (1972), Bayes Estimates for the Linear Model, Journal of the Royal Statistical Society B, 34, 1-41. | MR | Zbl

Lindström M.J., Bates D.M. (1988), Newton-Raphson and EM algorithms for linear mixed effects models for repeated measures data, Journal of the American Statistical Association, 83, 1014-1022. | MR | Zbl

Liu C., Rubin D.B. (1994), The ECME algorithm : a simple extension of the EM and ECM with faster monotone convergence, Biometrika, 81, 633-648. | MR | Zbl

Liu C., Rubin D.B., Wu Y.N. (1998), Parameter expansion to accelerate EM : the PX-EM algorithm, Biometrika, 85, 755-770. | MR | Zbl

Liu J.S., Wu Y.N. (1999), Parameter expansion scheme for data augmentation, Journal of the American Statistical Association, 94, 1264-1274. | MR | Zbl

Louis T.A. (1982), Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society B, 44, 226-233. | MR | Zbl

Mclachlan G.J., Bashford K.E. (1988) Mixture models : inferences and applications to clustering, Marcel Dekker, New York. | MR | Zbl

Mclachlan G.J., Krishnan T. (1997), The EM algorithm and extensions, John Wiley & Sons, New York. | MR | Zbl

Mclachlan G.J., Peel D. (2000), Finite mixture models, John Wiley & Sons, New York. | MR

Meng X.L. (2000) Missing data : dial M for ? ? ?, Journal of the American Statistical Association, 95, 1325-1330. | MR | Zbl

Meng X.L., Rubin D.B. (1991), Using EM to obtain asymptotic variance-covariance matrices : the SEM algorithm, Journal of the American Statistical Association, 86, 899-909.

Meng X.L., Rubin D.B. (1993), Maximum likelihood estimation via the ECM algorithm : a general framework, Biometrika, 80, 267-278. | MR | Zbl

Meng X.L., Van Dyk D.A. (1997), The EM algorithm-an Old Folk-song Sung to a Fast New Tune, Journal of the Royal Statistical Society B 59, 511-567. | MR | Zbl

Meng X.L., Van Dyk D.A. (1998), Fast EM-type implementations for mixed effects models, Journal of the Royal Statistical Society B 60, 559-578. | MR | Zbl

Nair V.N., Pregibon D. (1988), Analyzing dispersion effects from replicated factorial experiments, Technometrics, 30, 247-257. | MR | Zbl

Nicolas P., Bize L., Muri F., Hoebeke M., Rodolphe F., Ehrlich S., Prum B., Bessières P. (2002), Mining bacillus subtilis chromosome heterogeneities using hidden Markov models, Nucleic Acid Research, 30, 1418-1426.

Nielsen S.F. (2000), The stochastic EM algorithm : estimation and asymptotic results, Bernoulli, 6, 457-489. | MR | Zbl

Patterson H.D., Thompson R. (1971), Recovery of inter-block information when block sizes are unequal, Biometrika, 58, 545-554. | MR | Zbl

Rao C.R. (1973), Linear Statistical Inference and its Applications, 2nd édition. Wiley, New-York. | MR | Zbl

Rao C.R., Kleffe J. (1988), Estimation of variance components and applications, North Holland series in statistics and probability, Elsevier, Amsterdam. | MR | Zbl

Robert-Granié C., Ducrocq V., Foulley J.L. (1997), Heterogeneity of variance for type traits in the Montbéliarde cattle. Genetics Selection Evolution, 29, 545-570.

Robert-Granié C., Bonaiti B., Boichard D., Barbat A. (1999), Accounting for variance heterogeneity in French dairy cattle genetic evaluation, Livestock Production Science, 60, 343-357.

Robert-Granié C., Heude B., Foulley J.L. (2002), Modelling the growth curve of Maine Anjou beef cattle using heteroskedastic random regression models. Genetics Selection Evolution, 34, 423-445.

Robert C.P. (1996), Mixtures of distributions : inference and estimation, In Markov Chain Monte Carlo in Practice (Gilks W.R., Ricardson S., Spiegelhalter D.J., editors), Chapman & Hall, London, 441-464. | MR | Zbl

Robert C.P., Casella G. (1999), Monte Carlo Statistical Methods, Springer, Berlin. | MR | Zbl

San Cristobal M., Robert-Granié C., Foulley J.L. (2002), Hétéroscédasticité et modèles linéaires mixtes : théorie et applications en génétique quantitative, Journal de la Société Française de Statistiques, 143, 155-165.

Searle S.R. (1992), Matrix algebra useful for statistics, J. Wiley and Sons, New-York. | MR | Zbl

Searle S.R., Casella G., Mc Culloch C.E. (1992), Variance components, J. Wiley and Sons, New-York. | MR | Zbl

Smith S.P., Graser H.U. (1986), Estimating variance components in a class of mixed models by restricted maximum likelihood, Journal of Dairy Science, 69, 1156-1165.

Tanner M.A. (1996), Tools for Statistical Inference : Methods for the Exploration of Posterior Distributions and Likelihood Functions, Springer, New York. | MR | Zbl

Tanner M.A., Wong W.H. (1987), The calculation of posterior distributions by Data Augmentation (with discussion), Journal of the American Statistical Association, 82, 528-550. | MR | Zbl

Titterington D.M. (1984), Recursive parameter estimation using incomplete data, Journal of the Royal Statistical Society B, 46, 257-267. | MR | Zbl

Titterington D.M., Smith A.F.M., Makov U.E. (1985), Statistical Analysis of Finite Mixture, John Wiley & Sons, New York. | MR

Thompson R. (2002), A review of genetic parameter estimation, Proceedings of the 7 th World Congress of Genetics applied to Livestock Production, Montpellier, France, 19-23 August 2002.

Van Dyk D.A. (2000), Fitting mixed-effects models using efficient EM-type algorithms, Journal of Computational and Graphical Statistics, 9, 78-98. | MR

Van Dyk D.A, Meng X.L. (2001), The art of data augmentation, Journal of Computational and Graphical Statistics 10, 1-50. | MR

Wei G.C.G., Tanner M.A. (1990), A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms, Journal of the American Statistical Association, 85, 699-704.

Weir B.S. (1996), Genetic data analysis II, Sinauer associates, Sunderland, Massachussets.

Wolfinger R.D., Tobias R.D. (1998), Joint estimation of location, dispersion, and random effects in robust design, Technometrics, 40, 62-71. | Zbl

Wu C.F.J. (1983), On the convergence properties of the EM algorithm. Annals of Statistics, 11, 95-103. | MR

Wu R., Ma C-X., Little R.C., Casella G. (2002), A statistical model for the genetic origin of allometric scaling laws in biology, Journal of Theoretical Biology, 219, 121-135.