On finite mixture models

References

• Baum, L. E., Petrie, T., Soules, G., & Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics, 41(1), 164–171.
   Google Scholar
• Böhning, D. (2000). Computer-assisted analysis of mixtures and applications: Meta-analysis, disease mapping and others. London, UK: Chapman and Hall.
   Google Scholar
• Chen, H., & Chen, J. (2001). The likelihood ratio test for homogeneity in finite mixture models. Canadian Journal of Statistics, 29(2), 201–215.
   Web of Science ®Google Scholar
• Chen, H., & Chen, J. (2003). Tests for homogeneity in normal mixtures in the presence of a structural parameter. Statistica Sinica, 13, 351–365.
   Web of Science ®Google Scholar
• Chen, H., Chen, J., & Kalbfleisch, J. D. (2001). A modified likelihood ratio test for homogeneity in finite mixture models. Journal of the Royal Statistical Society: Series B, 63(1), 19–29.
   Google Scholar
• Chen, H., Chen, J., & Kalbfleisch, J. D. (2004). Testing for a finite mixture model with two components. Journal of the Royal Statistical Society: Series B, 66, 95–115.
   Google Scholar
• Chen, J. (1995). Optimal rate of convergence for finite mixture models. The Annals of Statistics, 23, 221–233.
   Web of Science ®Google Scholar
• Chen, J. (1998). Penalized likelihood-ratio test for finite mixture models with multinomial observations. Canadian Journal of Statistics, 26(4), 583–599.
   Web of Science ®Google Scholar
• Chen, J. (2016). Consistency of the mle under mixture models. Statistical Science. arXiv: 1607.01251.
   Web of Science ®Google Scholar
• Chen, J., & Cheng, P. (2000). The limiting distribution of the restricted likelihood ratio statistic for finite mixture models. Chinese Journal of Applied Probability and Statistics, 2, 159–167.
   Google Scholar
• Chen, J., Huang, Y., & Wang, P. (2016). Composite likelihood under hidden Markov model. Statistica Sinica, 26(4), 1569–1586.
   Web of Science ®Google Scholar
• Chen, J., & Li, P. (2011). Tuning the em-test for finite mixture models. Canadian Journal of Statistics, 39(3), 389–404.
   Web of Science ®Google Scholar
• Chen, J., & Li, P. (2016). Testing the order of a normal mixture in mean. Communications in Mathematics and Statistics, 4(1), 21–38.
   Google Scholar
• Chen, J., Li, P., & Fu, Y. (2012). Inference on the order of a normal mixture. Journal of the American Statistical Association, 107(499), 1096–1105.
   Web of Science ®Google Scholar
• Chen, J., Tan, X., & Zhang, R. (2008). Inference for normal mixtures in mean and variance. Statistica Sinica, 18, 443–465.
   Web of Science ®Google Scholar
• Chernoff, H., & Lander, E. (1995). Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial. Journal of Statistical Planning and Inference, 43(1), 19–40.
   Web of Science ®Google Scholar
• Dacunha-Castelle, D., & Gassiat, E. (1999). Testing the order of a model using locally conic parametrization: Population mixtures and stationary arma processes. The Annals of Statistics, 27(4), 1178–1209.
   Web of Science ®Google Scholar
• Dannemann, J., & Holzmann, H. (2008a). Likelihood ratio testing for hidden Markov models under non-standard conditions. Scandinavian Journal of Statistics, 35(2), 309–321.
   Web of Science ®Google Scholar
• Dannemann, J., & Holzmann, H. (2008b). Testing for two states in a hidden Markov model. Canadian Journal of Statistics, 36(4), 505–520.
   Web of Science ®Google Scholar
• Davies, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 64(1), 247–254.
   Google Scholar
• Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74(1), 33–43.
   Web of Science ®Google Scholar
• Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B, 39, 1–38.
   Google Scholar
• Engel, C. (1994). Can the Markov switching model forecast exchange rates? Journal of International Economics, 36(1–2), 151–165.
   Web of Science ®Google Scholar
• Friedlander, Y., & Leitersdorf, E. (1995). Segregation analysis of plasma lipoprotein (a) levels in pedigrees with molecularly defined familial hypercholesterolemia. Genetic Epidemiology, 12(2), 129–143.
   Web of Science ®Google Scholar
• Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York, NY: Springer Science & Business Media.
   Google Scholar
• Ghosh, J. K., & Sen, P. K. (1985). On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results. In L. LeCam & R. A. Olshen’ (Eds.), Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer (Vol. 2, pp. 789–806). Belmont, CA: Wadsworth.
   Google Scholar
• Hamilton, J. D. (2010). Regime switching models. In Macroeconometrics and time series analysis (pp. 202–209). London, UK: Palgrave Macmillan.
   Google Scholar
• Hartigan, J. A. (1985). A failure of likelihood asymptotics for normal mixtures. In L. LeCam & R. A. Olshen’ (Eds.), Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer (Vol. 2, pp. 807–810). Belmont, CA: Wadsworth.
   Google Scholar
• Hathaway, R. J. (1985). A constrained formulation of maximum-likelihood estimation for normal mixture distributions. The Annals of Statistics, 13, 795–800.
   Web of Science ®Google Scholar
• Holzmann, H., & Schwaiger, F. (2016). Testing for the number of states in hidden Markov models. Computational Statistics and Data Analysis, 100, 318–330.
   Web of Science ®Google Scholar
• Kiefer, J., & Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. The Annals of Mathematical Statistics, 27, 887–906.
   Google Scholar
• Lemdani, M., & Pons, O. (1999). Likelihood ratio tests in contamination models. Bernoulli, 5(4), 705–719.
   Web of Science ®Google Scholar
• Li, P., & Chen, J. (2010). Testing the order of a finite mixture. Journal of the American Statistical Association, 105(491), 1084–1092.
   Web of Science ®Google Scholar
• Li, P., Chen, J., & Marriott, P. (2009). Non-finite fisher information and homogeneity: An EM approach. Biometrika, 96, 411–426.
   Web of Science ®Google Scholar
• Li, S., Chen, J., Guo, J., Jing, B.-Y., Tsang, S.-Y., & Xue, H. (2015). Likelihood ratio test for multi-sample mixture model and its application to genetic imprinting. Journal of the American Statistical Association, 110(510), 867–877.
   Web of Science ®Google Scholar
• Lindsay, B. G. (1988). Composite likelihood methods. Contemporary Mathematics, 80(1), 221–239.
   Google Scholar
• Lindsay, B. G. (1995). Mixture models: Theory, geometry and applications. In NSF-CBMS regional conference series in probability and statistics. Hayward, CA: Institute of Mathematical Statistics.
   Google Scholar
• Liu, X., & Shao, Y. (2003). Asymptotics for likelihood ratio tests under loss of identifiability. Annals of Statistics, 31, 807–832.
   Web of Science ®Google Scholar
• McLachlan, G., & Peel, D. (2004). Finite mixture models. New York, NY: John Wiley & Sons.
   Google Scholar
• Morris, C. N. (1982). Natural exponential families with quadratic variance functions. The Annals of Statistics, 10, 65–80.
   Web of Science ®Google Scholar
• Neyman, J., & Scott, E. (1965). On the use of c (alpha) optimal tests of composite hypotheses. Bulletin of the International Statistical Institute, 41(1), 477–497.
   Google Scholar
• Niu, X., Li, P., & Zhang, P. (2011). Testing homogeneity in a multivariate mixture model. Canadian Journal of Statistics, 39(2), 218–238.
   Web of Science ®Google Scholar
• Ott, J. (1999). Analysis of human genetic linkage. Baltimore, MD: JHU Press.
   Google Scholar
• Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London A, 185, 71–110.
   Google Scholar
• Schork, N. J., Allison, D. B., & Thiel, B. (1996). Mixture distributions in human genetics research. Statistical Methods in Medical Research, 5(2), 155–178.
   Google Scholar
• Shen, J., & He, X. (2015). Inference for subgroup analysis with a structured logistic-normal mixture model. Journal of the American Statistical Association, 110(509), 303–312.
   Web of Science ®Google Scholar
• Titterington, D. M., Smith, A. F., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York, NY: Wiley.
   Google Scholar
• Varin, C. (2008). On composite marginal likelihoods. AStA – Advances in Statistical Analysis, 92(1), 1–28.
   Web of Science ®Google Scholar
• Varin, C., Reid, N., & Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21, 5–42.
   Web of Science ®Google Scholar
• Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 9(1), 60–62.
   Google Scholar
• Wu, C. J. (1983). On the convergence properties of the em algorithm. The Annals of statistics, 11, 95–103.
   Web of Science ®Google Scholar