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Research Article

EM-test for homogeneity in location-scale mixture model with a structural scale

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Received 19 Sep 2022, Accepted 27 Aug 2023, Published online: 08 Sep 2023

References

  • Bartlett, M. S. 1937. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences 160 (901):268–82.
  • Chen, H., and J. Chen. 2001. The likelihood ratio test for homogeneity in finite mixture models. Canadian Journal of Statistics 29 (2):201–15. doi: 10.2307/3316073.
  • Chen, H., and J. Chen. 2003. Tests for homogeneity in normal mixtures in the presence of a structural parameter. Statistica Sinica 13:351–65.
  • Chen, H., J. Chen, and J. D. Kalbfleisch. 2001. A modified likelihood ratio test for homogeneity in finite mixture models. Journal of the Royal Statistical Society Series B: Statistical Methodology 63 (1):19–29. doi: 10.1111/1467-9868.00273.
  • Chen, H., J. Chen, and J. D. Kalbfleisch. 2004. Testing for a finite mixture model with two components. Journal of the Royal Statistical Society Series B: Statistical Methodology 66 (1):95–115. doi: 10.1111/j.1467-9868.2004.00434.x.
  • Chen, J. 1995. Optimal rate of convergence for finite mixture models. The Annals of Statistics 23 (1):221–33. doi: 10.1214/aos/1176324464.
  • Chen, J. 1998. Penalized likelihood-ratio test for finite mixture models with multinomial observations. Canadian Journal of Statistics 26 (4):583–99. doi: 10.2307/3315719.
  • Chen, J. 2017. On finite mixture models. Statistical Theory and Related Fields 1 (1):15–27. doi: 10.1080/24754269.2017.1321883.
  • Chen, J., and J. D. Kalbfleisch. 2005. Modified likelihood ratio test in finite mixture models with a structural parameter. Journal of Statistical Planning and Inference 129 (1–2):93–107. doi: 10.1016/j.jspi.2004.06.041.
  • Chen, J., and P. Li. 2009. Hypothesis test for normal mixture models: The EM approach. The Annals of Statistics 37 (5A):2523–42. doi: 10.1214/08-AOS651.
  • Chen, J., and P. Li. 2011. Tuning the EM-test for finite mixture models. Canadian Journal of Statistics 39 (3):389–404. doi: 10.1002/cjs.10122.
  • Chen, J., and P. Li. 2016. Testing the order of a normal mixture in mean: A tribute to Professor Xiru Chen. Communications in Mathematics and Statistics 4 (1):21–38. doi: 10.1007/s40304-015-0079-5.
  • Chen, J., P. Li, and Y. Fu. 2012. Inference on the order of a normal mixture. Journal of the American Statistical Association 107 (499):1096–105. doi: 10.1080/01621459.2012.695668.
  • Chen, J., P. Li, and G. Liu. 2020. Homogeneity testing under finite location-scale mixtures. Canadian Journal of Statistics 48 (4):670–84. doi: 10.1002/cjs.11557.
  • Chen, J., P. Li, J. Qin, and T. Yu. 2021. Test for homogeneity with unordered paired observations. Electronic Journal of Statistics 15 (1):1661–94. doi: 10.1214/21-EJS1817.
  • Cordeiro, G. M., and F. Cribari-Neto. 2014. An introduction to Bartlett correction and bias reduction. New York: Springer Science & Business Media.
  • Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 39 (1):1–22. doi: 10.1111/j.2517-6161.1977.tb01600.x.
  • Gao, X., W. Shen, J. Ning, Z. Feng, and J. Hu. 2022. Addressing patient heterogeneity in disease predictive model development. Biometrics 78 (3):1045–55. doi: 10.1111/biom.13514.
  • Ghosh, J. K., and P. K. Sen. 1985. On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, 789–806.
  • Hartigan, J. 1985. A failure of likelihood asymptotics for normal mixtures. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer 2:807–10.
  • Lawless, J. F. 2003. Statistical models and methods for lifetime data. 2nd ed. New York: John Wiley & Sons.
  • Lawley, D. N. 1956. A general method for approximating to the distribution of likelihood ratio criteria. Biometrika 43 (3–4):295–303. doi: 10.1093/biomet/43.3-4.295.
  • Le Cam, L., and G. L. Yang. 1990. Asymptotics in statistics: Some basic concepts. New York: Springer-Verlag.
  • Li, P., and J. Chen. 2010. Testing the order of a finite mixture. Journal of the American Statistical Association 105 (491):1084–92. doi: 10.1198/jasa.2010.tm09032.
  • Li, P., J. Chen, and P. Marriott. 2009. Non-finite Fisher information and homogeneity: An EM approach. Biometrika 96 (2):411–26. doi: 10.1093/biomet/asp011.
  • Li, P., Y. Liu, and J. Qin. 2017. Semiparametric inference in a genetic mixture model. Journal of the American Statistical Association 112 (519):1250–60. doi: 10.1080/01621459.2016.1208614.
  • Li, P., and J. Qin. 2011. A new nuisance-parameter elimination method with application to the unordered homologous chromosome pairs problem. Journal of the American Statistical Association 106 (496):1476–84. doi: 10.1198/jasa.2011.tm10670.
  • Li, X., X. Zhou, and L. Tian. 2013. Interval estimation for the mean of lognormal data with excess zeros. Statistics & Probability Letters 83 (11):2447–53. doi: 10.1016/j.spl.2013.07.004.
  • Liu, G., Y. Fu, P. Li, and X. Pu. 2018. Using differential variability to increase the power of the homogeneity test in a two-sample problem. Statistica Sinica 28:27–41. doi: 10.5705/ss.202016.0026.
  • Liu, G., P. Li, Y. Liu, and X. Pu. 2019. On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter. Journal of Statistical Planning and Inference 199:29–44. doi: 10.1016/j.jspi.2018.05.003.
  • Naya, S., R. Cao, I. L. de Ullibarri, R. Artiaga, F. Barbadillo, and A. García. 2006. Logistic mixture model versus Arrhenius for kinetic study of material degradation by dynamic thermogravimetric analysis. Journal of Chemometrics 20 (3–4):158–63. doi: 10.1002/cem.1023.
  • Qin, X., J. S. Zhang, and X. D. Yan. 2012. Two improved mixture Weibull models for the analysis of wind speed data. Journal of Applied Meteorology and Climatology 51 (7):1321–32. doi: 10.1175/JAMC-D-11-0231.1.
  • Serfling, R. J. 1980. Approximation theorems of mathematical statistics. New York: John Wiley & Sons.
  • Van der Vaart, A. W. 2000. Asymptotic statistics. New York: Cambridge University Press.
  • Wu, C. J. 1983. On the convergence properties of the EM algorithm. The Annals of Statistics 11 (1):95–103. doi: 10.1214/aos/1176346060.

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