Root selection in normal mixture models

Computational Statistics and Data Analysis

Volumn 56, Issue 8, 2012, Pages 2454-2470

  Seo, Byungtae ^a   Kim, Daeyoung ^b  

^a Sungkyunkwan University   (South Korea)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Consistency; Maximum likelihood; Normal mixture; Singularity; Spurious local maximizer

Indexed keywords

CONSISTENCY; FINITE MIXTURES; FINITE NORMAL MIXTURES; GROUP STRUCTURE; LIKELIHOOD EQUATION; METHOD OF MAXIMUM LIKELIHOOD; MULTIPLE ROOTS; NORMAL MIXTURE MODELS; NORMAL MIXTURES; REAL EXAMPLE; SIMULATION STUDIES; SINGULARITY; SPURIOUS LOCAL MAXIMIZER; STATISTICAL INFERENCE;

COMPUTATIONAL METHODS; DATA HANDLING; MAXIMUM LIKELIHOOD;

MIXTURES;

EID: 84862789316     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.01.022     Document Type: Article

References (31)

1. C. Biernacki, and S. Chrétien Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM Statistics & Probability Letters 61 2003 373 382
2. D. Bhning, E. Dietz, R. Schaub, P. Schlattmann, and B.G. Lindsay The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family Annals of the Institute of Statistical Mathematics 46 1994 373 388
3. J. Chen, and X. Tan Inference for multivariate normal mixtures Journal of Multivariate Analysis 100 2009 1367 1383
4. J. Chen, X. Tan, and R. Zhang Consistency of penalized MLE for normal mixtures in mean and variance Statistica Sinica 18 2008 443 465
5. G.A. Ciuperca, A. Ridolfi, and J. Idier Penalized maximum likelihood estimator for normal mixtures Scandinavian Journal of Statistics 30 2003 45 59
6. S. Crawford, M.H. Degroot, J.B. Kadane, and M.J. Small Modeling lake chemistry distributions: approximate Bayesian methods for estimating a finite mixture model Technometrics 34 1992 441 453
7. A. Dempster, N. Laird, and D. Rubin Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society: Series B 39 1977 1 38
8. R.A. Fisher The use of multiple measurements in taxonomic problems Annals of Eugenics 7 1936 179 188
9. C. Fraley, and A.E. Raftery Bayesian regularization for normal mixture estimation and model-based clustering Journal of Classification 24 2007 155 181
10. S. Geman, and C. Hwang Nonparametric maximum likelihood estimation by the method of sieves Annals of Statistics 10 1982 401 414
11. U. Grenander Abstract Inference 1981 Wiley New York
12. J.D.F. Habbema, J. Hermans, and K. van den Broek A stepwise discriminant analysis program using density estimation Compstat 1974-Proceedings Computational Statistics 1974 Physica-Verlag Vienna 101 110
13. R.J. Hathaway A constrained formulation of maximum-likelihood estimation for normal mixture distributions Annals of Statistics 13 1985 795 800
14. R.J. Hathaway A constrained EM-algorithm for univariate normal mixtures Journal of Statistical Computation and Simulation 23 1986 211 230
15. C. Hennig Methods for merging Gaussian mixture components Advances in Data Analysis and Classification 4 2010 3 34
16. S. Ingrassia, and R. Rocci Constrained monotone EM algorithms for finite mixture of multivariate Gaussians Computational Statistics & Data Analysis 51 2007 5339 5351
17. A. Jasra, C.C. Holmes, and D.A. Stephens Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling Statistical Science 20 2005 50 67
18. J. Kiefer, and J. Wolfowitz Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters Annals of Mathematical Statistics 27 1956 886 906
19. Kim, D.; 2008. Mixture inference at the edge of identifiability. Ph.D. Thesis. Department of Statistics, The Pennsylvania State University.
20. Y. Linde, A. Buzo, and R. Gray An algorithm for vector quantizer design IEEE Transactions on Communications 28 1980 84 94
21. Lindsay, B.G.; 1995. Mixture models: theory, geometry, and applications. in: NSF-CBMS Regional Conference Series in Probability and Statistics, vol. 5. IMS: US.
22. R. Maitra, and V. Melnykov Simulating data to study performance of finite mixture modelling and clustering algorithms Journal of Computational and Graphical Statistics 19 2010 354 376
23. G.J. McLachlan, and K. Basford Mixture Models: Inference and Applications to Clustering 1988 Marcel Dekker New York
24. G.J. McLachlan, and D. Peel Finite Mixture Models 2000 John Wiley and Sons Ltd. New York
25. W. Seidel, and H. Sevckov Types of likelihood maxima in mixture models and their implication on the performance of tests Annals of the Institute of Statistical Mathematics 56 2004 631 654
26. Seo, B.; Kim, D.; 2012. Root selection in normal mixture models. Technical Report. http://www.math.umass.edu/~daeyoung/.
27. B. Seo, and B.G. Lindsay A computational strategy for doubly smoothed MLE exemplified in the normal mixture model Computational Statistics and Data Analysis 54 2010 1930 1941
28. K. Tanaka, and A. Takemura Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small Bernoulli 12 2006 1003 1017
29. D. Titterington, A.F.M. Smith, and U.E. Makov Statistical Analysis of Finite Mixture Distributions 1985 John Wiley & Sons New York
30. A. Wald Note on the consistency of the maximum likelihood estimate Annals of Mathematical Statistics 20 1949 595 601
31. W. Yao, and B.G. Lindsay Bayesian mixture labeling by highest posterior density Journal of the American Statistical Association 104 2009 758 767