Asymptotics for estimation and testing procedures under loss of identifiability

Journal of Multivariate Analysis

Volumn 97, Issue 1, 2006, Pages 19-45

  Zhu, Hongtu ^a   Zhang, Heping ^b  

^a New York State Psychiatric Institute ^*  (United States)

^b YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Asymptotic distribution; Cone; Convergence rate; Finite mixture models; Hellinger distance; Normal distribution

Indexed keywords

EID: 28044458989     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2004.11.005     Document Type: Article

References (23)

1. D.W.K. Andrews Generic uniform convergence Econometric Theory 8 1992 241-257
2. D.W.K. Andrews Tests for parameter instability and structural change with unknown change point Econometrica 61 1993 821-856
3. D.W.K. Andrews Estimation when a parameter is on a boundary: Theory and applications Econometrica 67 1999 1341-1383
4. D.W.K. Andrews Testing when a parameter is on the boundary of the maintained hypothesis Econometrica 69 2001 685-734
5. J. Chen Optimal rate of convergence for finite mixture models Ann. Statist. 23 1995 221-233
6. H. Chen J. Chen Tests for homogeneity in normal mixtures with presence of a structural parameter Statist. Sinica 13 2003 351-365
7. H. Chen J. Chen J. Kalbfleish A modified likelihood ratio test for homogeneity in finite mixture models J. Roy. Statist. Soc. B 63 2001 19-29
8. H. Chen J. Chen J.D. Kalbfleisch Testing for a finite mixture model with two components J. Roy. Statist. Soc. B 66 2004 95-115
9. D. Dachunha-Castelle E. Gassiat Testing the order of a model using locally conic parameterization: Population mixtures and stationary ARMA processes Ann. Statist. 27 1999 1178-1209
10. Z.D. Feng C.E. McCulloch Using bootstrap likelihood ratio in finite mixture models J. Roy. Statist. Soc. B 58 1996 609-617
11. B. Goffinet P. Loisel B. Laurent Testing in normal mixture models when the proportions are known Biometrika 79 1992 842-946
12. B.G. Lindsay, Mixture Models: Theory, Geometry and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, vol. 5. IMS, Hayward, CA, 1995.
13. X. Liu Y.Z. Shao Asymptotics for the likelihood ratio test under loss of identifiability Ann. Statist. 31 2003 807-832
14. P. Loisel B. Goffinet H. Monod G. Montes De Oca Detecting a major gene in an F2 population Biometrics 50 1994 512-516
15. G. McLachlan D. Peel Finite Mixture Models 2000 Wiley New York
16. M.D. Perlman One-sided testing problems in multivariate analysis Ann. Math. Statist. 40 1969 549-567
17. D. Pollard Convergence of Stochastic Processes 1984 Springer New York
18. D. Pollard, Empirical Processes: Theory and Applications, CBMS Regional Conference Series in Probability and Statistics, vol. 2, Institute of Mathematical Statistics, Hayward, CA, 1990.
19. T. Robertson F.T. Wright R.L. Dykstra Order Restricted Statistical Inference 1988 Wiley New York
20. D.M. Titterington A.F.M. Smith U.E. Markov Statistical Analysis of Finite Mixture Models 1985 Wiley New York
21. H.P. Zhang K. Merikangas A frailty model of segregation analysis: understanding the familial transmission of alcoholism Biometrics 56 2000 815-823
22. H.P. Zhang R. Feng H.T. Zhu A latent variable model of segregation analysis for ordinal traits J. Amer. Statist. Assoc. 98 2003 1023-1034
23. H.T. Zhu, H.P. Zhang, Hypothesis testing in mixture regression models (mathematical details), Technical Report, Yale University School of Medicine, New Haven, 2004.