Asymptotics for the likelihood ratio test in a two-component normal mixture model

Journal of Statistical Planning and Inference

Volumn 123, Issue 1, 2004, Pages 61-81

  Liu, Xin ^a   Shao, Yongzhao ^b,c  

^a ROCKEFELLER UNIVERSITY   (United States)

^b Columbia University ^*  (United States)

^c NEW YORK UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Asymptotic distribution; Gaussian mixture model; Homogeneity test; Likelihood ratio test

Indexed keywords

EID: 1642265259     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(03)00138-1     Document Type: Article

References (18)

1. Bickel P. Chernoff H. 1993 Asymptotic distribution of the likelihood ratio statistic in a prototypical non regular problem. In: Ghosh, et al. (Eds.), Statistics and Probability: A Raghu Raj Bahadur Festschrift, Wiley Eastern Limited, New Delhi, pp. 83-96.
2. Böhning D. Dietz E. Schaub R. Schlattman P. Lindsay B.G. The distribution of the likelihood ratio for mixtures of densities from the one parameter exponential family Ann. Inst. Statist. Math. 46 1994 373-388
3. Chen H. Chen J. Large sample distribution of the likelihood ratio test for normal mixtures Statist. Probab. Lett. 52 2001 125-133
4. Csörgo M. Révész P. Strong Approximations in Probability and Statistics 1981 Academic Press New York
5. Csörgo M. Csörgo S. Horváth L. Mason D.M. Weighted empirical and quantile processes Ann. Probab. 14 1986 31-85
6. Davies R. Hypothesis testing when a nuisance parameter is present only under the alternative Biometrika 64 1977 247-254
7. Garel B. Likelihood ratio test for univariate Gaussian mixture J. Statist. Plann. Inference 96 2001 325-350
8. Hartigan J.A. 1985 A failure of likelihood ratio asymptotics for normal mixtures. In: Le Cam, L., Olshen, A. (Eds.), Proceedings of Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II. Wadsworth Advanced Books, Monterey, CA.
9. Lindsay B.G. Mixture models: theory, geometry and applications NSF-CBMS Regional Conference Series in Probability and Statistics Vol. 5 1995 IMS, Hayward California
10. Liu X. Shao Y. 2003 Asymptotics for the likelihood ratio test under loss of identifiability. Ann. Statist. 31, in press.
11. Liu X. Pasarica C. Shao Y. 2003 Testing homogeneity in Gamma mixture models. Scand. J. Statist. 30, 227-239.
12. McLachlan G.J. Basford K.E. Mixture Models: Inference and Applications to Clustering 1988 Dekker New York
13. Pollard D. Asymptotics via empirical processes Statist. Sci. 4 1989 341-366
14. Shorack G.R. Wellner J.A. Empirical Processes with Applications to Statistics 1986 Wiley New York
15. Thode H.C. Finch S.J. Mendell N.R. Simulation percentage points for the null distribution of the likelihood ratio test for a mixture of two normals Biometrics 44 1988 1195-1201
16. Titterington D.M. Smith A.F.M. Makov U.E. Statistical Analysis of Finite Mixture Distributions 1985 Wiley New York
17. van der Vaart A.W. Wellner J.A. Weak Convergence and Empirical Processes with Applications to Statistics 1996 Springer New York
18. Xu Y. 1997 Unidentifiable asymptotic problems. Ph.D. Thesis, Yale University.