Variable selection in finite mixture of generalized estimating equations

References

• Allman, E. S., C. Matias, and J. A. Rhodes. 2009. Identifiability of parameters in latent structure models with many observed variables. The Annals of Statistics 37 (6A):3099–132. doi:10.1214/09-AOS689.
   Web of Science ®Google Scholar
• Carroll, R. J., and P. Hall. 1988. Optimal rates of convergence for deconvolving a density. Journal of the American Statistical Association 83 (404):1184–6. doi:10.2307/2290153.
   Web of Science ®Google Scholar
• DasGupta, A. 2008. Mixture Models and Nonparametric Deconvolution. In Asymptotic Theory of Statistics and Probability, 571–91. New York: Springer.
   Google Scholar
• De Veaux, R. D. 1989. Mixtures of linear regressions. Computational Statistics & Data Analysis 8 (3):227–45. doi:10.1016/0167-9473(89)90043-1.
   Web of Science ®Google Scholar
• Dias, J. G., and M. Wedel. 2004. An empirical comparison of EM, SEM and MCMC performance for problematic Gaussian mixture likelihoods. Statistics and Computing 14 (4):323–32. doi:10.1023/B:STCO.0000039481.32211.5a.
   Web of Science ®Google Scholar
• Elmore, R., P. Hall, and A. Neeman. 2005. An application of classical invariant theory to identifiability in nonparametric mixtures. Annales de l’institut Fourier 55 (1):1–28. doi:10.5802/aif.2087.
   Web of Science ®Google Scholar
• Eskandari, F., and E. Ormoz. 2016. Finite mixture of generalized semiparametric models: variable selection via penalized estimation. Communications in Statistics - Simulation and Computation 45 (10):3744–59. doi:10.1080/03610918.2014.953687.
   Web of Science ®Google Scholar
• Fan, J. 1991. On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics 19 (3):1257–72. doi:10.1214/aos/1176348248.
   Web of Science ®Google Scholar
• Faria, S., and G. Soromenho. 2010. Fitting mixtures of linear regressions. Journal of Statistical Computation and Simulation 80 (2):201–25. doi:10.1080/00949650802590261.
   Web of Science ®Google Scholar
• Faria, S., and G. Soromenho. 2012. Comparison of EM and SEM algorithms in Poisson regression models: a simulation study. Communications in Statistics - Simulation and Computation 41 (4):497–509. doi:10.1080/03610918.2011.594534.
   Web of Science ®Google Scholar
• Hall, P., A. Neeman, R. Pakyari, and R. Elmore. 2005. Nonparametric inference in multivariate mixtures. Biometrika 92 (3):667–78. doi:10.1093/biomet/92.3.667.
   Web of Science ®Google Scholar
• Hall, P., and X. H. Zhou. 2003. Nonparametric estimation of component distributions in a multivariate mixture. The Annals of Statistics 31 (1):201–24. doi:10.1214/aos/1046294462.
   Web of Science ®Google Scholar
• Hawkins, D. S., D. M. Allen, and A. J. Stromberg. 2001. Determining the number of components in mixtures of linear models. Computational Statistics & Data Analysis 38 (1):15–48. doi:10.1016/S0167-9473(01)00017-2.
   Web of Science ®Google Scholar
• Jones, P. N., and G. J. McLachlan. 1992. Fitting finite mixture models in a regression context. Australian Journal of Statistics 34 (2):233–40. doi:10.1111/j.1467-842X.1992.tb01356.x.
   Google Scholar
• Nguyen, X. 2013. Convergence of latent mixing measures in finite and infinite mixture models. The Annals of Statistics 41 (1):370–400. doi:10.1214/12-AOS1065.
   Web of Science ®Google Scholar
• Pearson, K. 1894. Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London. A 185:71–110. doi:10.1098/rsta.1894.0003.
   Google Scholar
• Quandt, R. E., and J. B. Ramsey. 1978. Estimating mixtures of normal distributions and switching regressions. Journal of the American Statistical Association 73 (364):730–8. doi:10.2307/2286266.
   Web of Science ®Google Scholar
• Rousseau, J., and K. Mengersen. 2011. Asymptotic behaviour of the posterior distribution in overfitted mixture models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (5):689–710. doi:10.1111/j.1467-9868.2011.00781.x.
   Google Scholar
• Schepers, J. 2015. Improved random-starting method for the EM algorithm for finite mixtures of regressions. Behavior Research Methods 47 (1):134–46.
   PubMed Web of Science ®Google Scholar
• Searle, S. R. 1997. Linear models. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• Teicher, H. 1961. Identifiability of mixtures. The Annals of Mathematical Statistics 32 (1):244–8.
   Google Scholar
• Teicher, H. 1963. Identifiability of finite mixtures. The Annals of Mathematical Statistics 34 (4):1265–9. doi:10.1214/aoms/1177703862.
   Google Scholar
• Xu, L., N. Lin, B. Zhang, and N. Shi. 2012. A Finite mixture model for working correlation matrices in generalized estimating equations. Statistica Sinica 22 (2):755–76. doi:10.5705/ss.2010.090.
   Web of Science ®Google Scholar
• Yakowitz, S. J., and J. D. Spragins. 1968. On the identifiability of finite mixtures. The Annals of Mathematical Statistics 39 (1):209–14. doi:10.1214/aoms/1177698520.
   Google Scholar
• Zhang, C. H. 1990. Fourier methods for estimating mixing densities and distributions. The Annals of Statistics 18 (2):806–31. doi:10.1214/aos/1176347627.
   Web of Science ®Google Scholar
• Zhu, H. T., and H. Zhang. 2004. Hypothesis testing in mixture regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66 (1):3–16. doi:10.1046/j.1369-7412.2003.05379.x.
   Web of Science ®Google Scholar