Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Estimating Parameters in Muitivariate Normal Mixtures

  • Received : 20110100
  • Accepted : 20110300
  • Published : 2011.05.31
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Abstract

This paper investigates a penalized likelihood method for estimating the parameter of normal mixtures in multivariate settings with full covariance matrices. The proposed model estimates the number of components through the addition of a penalty term to the usual likelihood function and the construction of a penalized likelihood function. We prove the consistency of the estimator and present the simulation results on the multi-dimensional nor-mal mixtures up to the 8-dimension.

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References

  1. Alexandridis, R., Lin, S. and Irwin, M. (2004). Class discovery and classification of tumor samples using mixture modeling of gene expression data-A unified approach, Biominfomatics, 20, 2545-2552. https://doi.org/10.1093/bioinformatics/bth281
  2. Chen, K. and Tan, X. (2009). Inference for multivariate normal mixtures, Journal of Multivariate Analysis, 100, 1367-1383. https://doi.org/10.1016/j.jmva.2008.12.005
  3. Ciuperca, G., Ridolfi, A. and Idier, J. (2003). Penalized maximum likelihood estimator for normal Mixtures, Scandinavian Journal of Statistics, 30, 45-59. https://doi.org/10.1111/1467-9469.00317
  4. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of Royal Statistical Society(B), 39, 1-38.
  5. Hathaway, R. J. (1985). A constrained formulation of maximum likelihood estimation for normal mixture distributions, Annals of Statistics, 13, 795-800. https://doi.org/10.1214/aos/1176349557
  6. Ingrassia, S. (2004). A likelihood-based constrained algorithm for multivariate normal mixture models, Statistical Methods & Applications, 13, 151-166.
  7. Priebe, C. E. (1994). Adaptive mixtures, Journal of American Statistical Association, 89, 796-806. https://doi.org/10.2307/2290905
  8. Raftery, A. E. and Dean, N. (1998). Variable selection for model-based clustering, Journal of American Statistical Association, 101, 168-178.
  9. Redner, R. (1981). Note on the consistency of the maximum likelihood estimate for nonidentifiable distributions, Annals of Statistics, 9, 225-228. https://doi.org/10.1214/aos/1176345353
  10. Roeder, K. and Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals, Journal of the American Statistical Association, 92, 894-902. https://doi.org/10.2307/2965553
  11. Solka, J. L., Poston, W. L. and Wegman, E. J. (1995). A visualization technique for studying the iterative estimation of mixture densities, Journal of Computational and Graphical Statistics, 4, 180-198. https://doi.org/10.2307/1390846
  12. Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985). Statistical Analysis of Finite Mixture Distributions, Wiley.
  13. Wald, A. (1949). Note on the consistency of the maximum likelihood estimate, Annals of Mathematical Statistics, 20, 595-601. https://doi.org/10.1214/aoms/1177729952

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