An effective method for selecting the number of components in density mixtures

Journal of Statistical Computation and Simulation

Volumn 77, Issue 10, 2007, Pages 907-914

  Whitaker, S ^a   Lee, T C M ^a  

^a Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Bootstrap; Density mixtures; Gaussian mixtures; Mixture distributions; Plug in principle; Unbiased risk estimation

Indexed keywords

EID: 34648814044     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/10629360600827263     Document Type: Article

References (22)

1. Redner, R.A. and Walker, H.F., 1984, Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26, 195-239.
2. Derin, H., 1987, Estimating components of univariate gaussian mixtures using Prony's method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9, 142-148.
3. Tadjudin, S. and Landgrebe, D.A., 2000, Robust parameter estimation for mixture model. IEEE Transactions on Geoscience and Remote Sensing, 38, 439-445.
4. Titterington, D.M., Smith, A.F.M. and Makov, U.E., 1985, Statistical Analysis of Finite Mixture Distributions (Chichester: John Wiley & Sons Ltd.).
5. McLachlan, G. and Basford, K., 1988, Mixture Models: Inference and Applications to Clustering (New York: Marcel Dekker).
6. Windham, M.P. and Cutler, A., 1992, Information ratios for validating mixture analyses. Journal of the American Statistical Association, 87, 1188-1192.
7. Crawford, S., 1994, An application of the laplace method to finite mixture distributions. Journal of the American Statistical Association, 89, 259-267.
8. Feng, Z.D. and McCulloch, C.E., 1996, Using bootstrap likelihood ratios in finite mixture models. Journal of the Royal Statistical Society Series B, 58, 609-617.
9. Polymenis, A. and Titterington, D.M., 1998, On the determination of the number of components in a mixture. Statistics and Probability Letters, 38, 295-298.
10. James, L.F., Priebe, CE. and Marchette, D.J., 2001, Consistent estimation of mixture complexity. The Annals of Statistics, 29, 1281-1296.
11. Chen, J. and Kalbfleisch, J.D., 1996, Penalized minimum-distance estimates in finite mixture models. Canadian Journal of Statistics, 24, 167-175.
12. Miloslavsky, M. and van der Laan, M.J., 2003, Fitting of mixtures with unspecified number of components using cross validation distance estimate. Computational Statistics and Data Analysis, 41, 413-428.
13. Escobar, M.D. and West, M., 1995, Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577-588.
14. Richardson, S. and Green, P., 1997, On Bayesian analysis of mixtures with, an unknown number of components. Journal of the Royal Statistical Society Series B, 59, 731-758.
15. Roeder, K. and Wasserman, L., 1997, Practical bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894-902.
16. Efron, B. and Tibshirani, R.J., 1993, An Introduction to the Bootstrap (New York: Champman and Hall).
17. Jones, M.C., Marron, J.S. and Sheather, S.J., 1996, A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, 91, 401-407.
18. Wand, M.P. and Gutierrez, R.G., 1997, Exact risk approaches to smoothing parameter selection. Journal of Nonparametric Statistics, 8, 337-354.
19. Lee, T.C.M., 2001, A stabilized bandwidth selection method for kernel smoothing of the periodogram. Signal Processing, 81, 419-430.
20. Schwarz, G., 1978, Estimating the dimension of a model. The Annals of Statistics, 6, 461-464.
21. Rissanen, J., 1989, Stochastic Complexity in Statistical Inquiry (Singapore: World Scientific).
22. Keribin, C., 2000, Consistent estimation of the order of mixture models. Sankhya, 62, 49-66.