References
- Charnigo, R., and J. Sun. 2004. Testing homogeneity in a mixture distribution via the l2 distance between competing models. Journal of the American Statistical Association 99 (466):488–98. doi:10.1198/016214504000000494.
- Chauveau, D., B. Garelz, and S. Mercier. 2019. Testing for univariate two-component Gaussian mixture in practice. Journal of the French Statistical Society 160:86–113.
- 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., 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., 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.
- Garel, B. 2001. Likelihood ratio test for univariate gaussian mixture. Journal of Statistical Planning and Inference 96 (2):325–50. doi:10.1016/S0378-3758(00)00216-0.
- Hartigan, J. A. 1985. A failure of likelihood asymptotics for normal mixtures. Proc. Bark. Conf. in Honor of J. Neyman and J. Kiefer 2:807–10.
- Le Cam, L. 1960. Locally asymptotically normal families of distributions. University of California Publications in Statistics 3:37–98.
- Liu, X., and Y. Shao. 2003. Asymptotics for likelihood ratio tests under loss of identifiability. The Annals of Statistics 31 (3):807–32. doi:10.1214/aos/1056562463.
- Mohri, M., A. Rostamizadeh, and A. Talwakar. 2018. Foundations of machine learning. 2nd ed. Boston: The MIT Press.
- Watanabe, S. 2001. Algebraic analysis for nonidentifiable learning machines. Neural Computation 13 (4):899–933. doi:10.1162/089976601300014402.
- Watanabe, S. 2018. Mathematical theory of Bayesian statistics. New York: Chapman and Hall/CRC.
- Watanabe, S., and S. Amari. 2003. Learning coefficients of layered models when the true distribution mismatches the singularities. Neural Computation 15 (5):1013–33. doi:10.1162/089976603765202640.