The EM algorithm with gradient function update for discrete mixtures with known (fixed) number of components

Statistics and Computing

Volumn 13, Issue 3, 2003, Pages 257-265

  Böhning, Dankmar ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Globally convergent algorithms; Mixture models; Multiple maxima

Indexed keywords

EID: 0347093592     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024222817645     Document Type: Article

References (16)

1. Böhning D. 1982. Convergence of Simar's algorithm for finding the maximum likelihood estimate of a compound Poisson process. Annals of Statistics 10: 1006-1008.
2. Böhning D. 2000. Computer-Assisted Analysis of Mixtures and Applications. Meta-Analysis, Disease Mapping and Others. Chapman & Hall/CRC, Boca Raton.
3. Carlin B.P. and Louis T.A. 2000. Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall, London.
4. Celeux G. 2001. Different points of view for choosing the number of components in a mixture model. In: Govaert G., Janssen J., and Limnios N. (Eds.), Proceedings of the 10th International Symposium on Applied Stochastic Models and Data Analysis, June 12-15. Compiegne, pp. 21-28.
5. Dempster A.P., Laird N.M., and Rubin D.B. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with Discussion). Journal of the Royal Statistical Society B 39: 1-38.
6. Fawzi W.W., Chalmers T.C., Herrera M.G., and Mosteller F. 1993. Vitamin A supplementation and child mortality. A meta-analysis. Journal of the American Medical Association 269: 898-903.
7. Hasselblad V 1969. Estimation of finite mixtures of distributions from the exponential family. Journal of the American Statistical Association 64: 1459-1471.
8. Laird N.M. 1978. Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association 73: 805-811.
9. Leroux B.G. 1992. Consistent estimation of a mixing distribution. Annals of Statistics 20: 1350-1360.
10. Lim, T.-O., Bakri R., Morad Z., and Hamid M.A. 2001. Bimodality in blood glucose distribution: Is it universal? Preprint of the Clinical Research Centre, c/o Department of Nephrology, Kualalumpur Hospital, Kualalumpur, Malaysia.
11. Lindsay B.G. 1983. The geometry of mixture likelihoods, Part I: A general theory. Annals of Statistics 11: 783-792.
12. Mclachlan G. and Peel D. 2000. Finite Mixture Models. Wiley, New York.
13. Seidel W., Mosler K., and Alker M. 2000. A cautionary note on likelihood ratio tests in mixture models. Annals of the Institute of Statistical Mathematics 52: 481-487.
14. Simar L. 1976. Maximum likelihood estimation of a compound Poisson process. Annals of Statistics 4: 1200-1209.
15. Thyrion P. 1960. Contribution à l'étude du bonus pour non sinsitre en assurance automobile. Astin Bulletin 1: 142-162.
16. Titterington D.M., Smith A.F.M., and Makov U.E. 1985. Statistical Analysis of Finite Mixture Distributions. Wiley, New York.