Fitting of Mixtures with unspecified number of components cross validation distance estimate

Computational Statistics and Data Analysis

Volumn 41, Issue 3-4, 2003, Pages 413-428

  Miloslavsky, Maja ^a   van der Laan, Mark J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cross validation; Minimum distance; Mixtures; Normal mixtures

Indexed keywords

COMPUTER SIMULATION; MONTE CARLO METHODS; NUMBER THEORY; OPTIMIZATION;

MIXTURE COMPONENTS;

PROBLEM SOLVING;

NUMERICAL METHOD;

EID: 0037469113     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(02)00166-4     Document Type: Article

References (33)

1. Aitkin, M., Rubin, D.B., 1985. Estimation and hypothesis testing in finite mixture models. J. Roy. Statist. Soc. Ser. B 47 (1), 67-75.
2. Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F. (Eds.), Second International Symposium on Information Theory. Academiai Kiado, Budapest, pp. 267-281.
3. Biernacki, C., Celeux, G., Govaert, G., 1999. An improvement on the nec criterion for assessing the number of clusters in a mixture model. Pattern Recognition Lett. 20, 267-272.
4. Black, D.M., Cummings, S.R., Karpf, D.B., Cauley, J.A., Thompson, D.E., Nevitt, M.C., Bauer, D.C., Genant, H.K., Haskell, W.L., Marcus, R., Ott, S.M., Torner, J.C., Quandt, S.A., Reiss, T.F., Ensrud, K.E., 1996. Randomised trial of effect of alendronate on risk of fracture in women with existing vertebral fracture. Lancet 348 (9041), 1535-1541.
5. Böhning, D., 1999. Computer-Assisted Analysis of Mixtures and Applications: Meta-Analysis, Disease Mapping and Others. Chapman & Hall, London.
6. Böhning, D., Dietz, E., Schaub, R., Schlattmann, P., Lindsay, B.G., 1994. The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family. Ann. Inst. Statist. Math. 46 (2), 373-388.
7. Bozdogan, H., 1993. Choosing the number of component clusters in the mixture-model using a new informational complexity criterion of the inverse-fisher information matrix. In: Opitz, O., Lausen, B., Klar, R. (Eds.), Information and Classification. Springer, Heidelberg, pp. 40-54.
8. Bozdogan, H., 2000. Akaike's information criterion and recent developments in information complexity. J. Math. Psych. 44, 62-91.
9. Celeux, G., Soromenho, G., 1996. An entropy criterion for assessing the number of clusters in a mixture model. J. Classification 13, 195-212.
10. Chen, J., Kalbfleisch, J.D., 1996. Penalised minimum distance estimates in finite mixture models. Canadian J. Statist. 24, 167-175.
11. Cummings, S.R., Black, D.M., Thompson, D.E., Applegate, W.B., Barrett-Connor, E., Musliner, T.A., Palermo, L., Prineas, R., Rubin, S.M., Scott, J.C., Vogt, T., Wallace, R., Yates, A.J., LaCroix, A.Z., 1998. Effect of alendronate on risk of fracture in women with low bone density but without vertebral fractures: results from the fracture intervention trial J. Amer. Med. Assoc. 280 (24), 2077-2082.
12. Everitt, B.S., Hand, D.J., 1981. Finite Mixture Distributions. Chapman & Hall, London, New York.
13. Feng, Z., McCulloch, C.E., 1992. Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space. Statist. Probab. Lett. 13, 325-332.
14. Feng, Z., McCulloch, C.E., 1994. On the likelihood ratio test statistic for the number of components in a normal mixture with unequal variances. Biometrics 50, 1158-1162.
15. Feng, Z., McCulloch, C.E., 1996. Using bootstrap likelihood ratios in finite mixture models. J. Roy. Statist. Soc. Ser. B 58 (3), 609-617.
16. Fraley, C., Raftery, A.E., 1998. How many clusters? which clustering method? answers via model-based cluster analysis. Comput. J. 41 (8), 578-588.
17. Hansen, M.H., Yu, B., 2001. Model selection and the principle of minimum description length. J. Amer. Statist. Assoc. 96, 746-774.
18. Henna, J., 1985. On estimating of the number of constituents of a finite mixture of continuous distributions. Ann. Inst. Statist. Math. 37 (2), 235-240.
19. Karpf, D.B., Shapiro, D.R., Seeman, E., Ensrud, K.E., Johnston Jr., C.C., Adami, S., Harris, S.T., Santora 2nd, A.C., Hirsch, L.J., Oppenheimer, L., Thompson, D., 1997. Prevention of nonvertebral fractures by alendronate. J. Amer. Med. Assoc. 277 (14), 1159-1164.
20. Keribin, C., 2000. Consistent estimation of the order of mixture models. Sankhya Ser. A 62, 49-66.
21. Lindsay, B.G., 1995. Mixture Models: Theory, Geometry, and Applications. Vol. 5, Regional Conference Series in Probability and Statistics. Institute of Mathematical Statistics and the American Statistical Association. Hayward, CA.
22. McLachlan, G.J., 1987. On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Appl. Statist. 36 (3), 318-324.
23. McLachlan, G.J., Basford, K.E., 1988. Mixture Models: Inference and Applications to Clustering. . Statistics, Textbooks and Monographs, Vol. 84. Marcel Dekker, New York.
24. McLachlan, G.J., Peel, D., 1997. On a resampling approach to choosing the number of components in normal mixture models. In: Billard, L., Fisher, N.I. (Eds.), Computing Science and Statistics: Graph-Image-Vision: Proceedings of the 28th Symposium on the Interface, Sydney, Australia, Vol. 28, Fairfax Station, VA, pp. 260-266, Interface Foundation of North America.
25. McLachlan, G., Peel, D., 2000. Finite Mixture Models. Wiley series in probability and statistics. Wiley, New York.
26. Mendell, N.R., Thode Jr., H.C., Finch, S.J., 1991. The likelihood ratio test for the two-component normal mixture problem: power and sample size analysis Biometrics 47, 1143-1148.
27. Pavlic, M., Brand, R., Cummings, S.M., 2001. Estimating probability of non-response to treatment using mixture distributions. Statist. Med. 20 (12), 1739-1753.
28. Richardson, S., Green, P.J., 1997. On Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc. Ser. B 59 (4), 731-758.
29. Smyth, P., 2000. Model selection for probabilistic clustering using cross-validated likelihood. Statist. Comput. 10 (1), 63-72.
30. Titterington, D.M., Smith, A.F.M., Makov, U.E., 1985. Statistical Analysis of Finite Mixture Distributions. Wiley series in probability and mathematical statistics, Wiley, New York.
31. Windham, M.P., Cutler, A., 1992. Information ratios for validating mixture analyses. J. Amer. Statist. Assoc. Theory Methods 87 (420), 1188-1192.
32. Windham, M.P., Cutler, A., 1994. Information-based validity functionals for mixture analysis. In: Bozdogan, H. (Ed.), Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: an Informational Approach. Kluwer Academic Publishers, Dordrecht, pp. 149-170.
33. Wolfe, J.H., 1971. A Monte Carlo study of the sampling distribution of the likelihood ratio for mixtures of multinomial distributions. Technical bulletin stb 72-2. US Naval Personnel and Training Research Laboratory, San Diego.