The consistency of estimators in finite mixture models

Scandinavian Journal of Statistics

Volumn 28, Issue 4, 2001, Pages 603-616

  Cheng, R C H ^b   Liu, Wenbin B ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

^b NONE

Author keywords

Embedded model; Indeterminacy; Maximum likelihood; Parametric bootstrap

Indexed keywords

EID: 0035647936     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00257     Document Type: Article

References (11)

1. Berman, M. (1986). Some unusual examples of extrema associated with hypothesis tests when nuiscance parameters are present under the alternative. In Proceedings of Pacific statistics congress (eds I. S. Francis, B. F. J. Manly & F. C. Lam), North Holland, Amsterdam.
2. Cheng, R. C. H. & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. J. Roy. Statist. Soc. Ser. B 45, 394-403.
3. Cheng, R. C. H. & Traylor, L. (1995). Non-regular maximum likelihood problems. J. Roy. Statist. Soc. Ser. B 57, 3-44.
4. Feng, Z. D. & McCulloch, C. E. (1996). Using bootstrap likelihood ratios in finite mixture models. J. Roy. Statist. Soc. Ser. B 58, 593-608.
5. 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 Proceedings of Berkeley symposium in honor of Neyman, J. and Kiefer, J. (eds L. LeCam & R. A. Olshen), Vol. II, 789-806, Wadsworth, New York.
6. Hartigan, J. A. (1985). A failure of likelihood asymptotics for the mixture model. In Proceedings of Berkeley symposium in honor of Neyman, J. and Kiefer, J. (eds L. LeCam & R. A. Olshen), Vol. II, 807-810. Wadsworth, New York.
7. Redner, R. (1981). Note on the consistency of the maximum likelihood estimate for nonidentifiable distributions. Ann. Statist. 9, 225-228.
8. Richardson, S. & Green, P. J. (1997). A Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc. Ser. B 59, 473-484.
9. Smith, R. L. (1989). A survey of nonregular problems. Proceedings of the International Statistical Institute conference, 47th session, Paris, 353-372.
10. Titterington, D. M., Smith, A. F. M. & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. Wiley, Chichester.
11. Wald, A. (1949). Note on the consistency of the maximum likelihood estimates. Ann. Math. Statist. 20, 595-601.