Edgeworth Expansion of the Moment-Based Test for Homogeneity in an NEF-QVF Mixture Model

References

• Bickel , P. J. and Chernoff , H. 1993 . “ Asymptotic distribution of the likelihood ratio statistic in a prototypical nonregular problem ” . In Statistics and Probability: A Raghu Raj Bahadur Festschrift , Edited by: Ghosh , J. K. , Mitra , S. K. , Parthasarathy , K. R. and Prakasa Rao , B. L. S. 83 – 96 . New York : Wiley .
   Google Scholar
• Chen , H. , Chen , J. H. and Kalbfleisch , J. D. 2001 . A modified likelihood ratio test for homogeneity in finite mixture models . Journal of the Royal Statistical Society: Series B , 63 : 19 – 29 .
   Google Scholar
• Chen , H. and Chen , J. H. 2001 . The likelihood ratio test for homegeneity in finite mixture models . Canadian Journal of Statistics , 29 : 201 – 215 .
   Web of Science ®Google Scholar
• Chernoff , H. and Lander , E. 1995 . Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial . Journal of Statistical Planning and Inference , 43 : 19 – 40 .
   Web of Science ®Google Scholar
• Chiano , M. N. and Yates , J. R. W. 1995 . Linkage detection under heterogeneity and the mixture problem . Annals of Human Genetics , 59 : 83 – 95 .
   PubMedGoogle Scholar
• Dacunha-Castelle , D. and Gassiat , E. 1999 . Testing the order of a model using locally conic parameterization: Population mixtures and stationary ARMA processes . Annals of Statistics , 27 : 1178 – 1209 .
   Web of Science ®Google Scholar
• Everitt , B. S. and Hand , D. J. 1981 . Finite Mixture Distributions , New York : Chapman and Hall .
   Google Scholar
• Faraway , J. J. 1993 . Distribution of the admixture test for the detection of linkage under heterogeneity . Genetic Epidemiology , 10 : 75 – 83 .
   PubMed Web of Science ®Google Scholar
• Garel , B. 2001 . Likelihood ratio test for univariate Gaussian mixture . Journal of Statistical Planning and Inference , 96 : 325 – 350 .
   Web of Science ®Google Scholar
• Ghosh , J. K. and Sen , P. K. 1985 . “ On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results ” . In In: Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer, Vol. 2. , 789 – 906 . Belmont : Wadesworth .
   Google Scholar
• Hall , P. 1992 . The Bootstrap and Edgeworth Expansion , New York : Springer-Verlag .
   Google Scholar
• Lemdani , M. and Pons , O. 1995 . Tests for genetic linkage and homogeneity . Biometrics , 51 : 1033 – 1041 .
   PubMed Web of Science ®Google Scholar
• Lemdani , M. and Pons , O. 1997 . Likelihood ratio tests for genetic linkage . Statistical and Probability Letters , 33 : 15 – 22 .
   Web of Science ®Google Scholar
• Lemdani , M. and Pons , O. 1999 . Likelihood ratio tests in contamination models . Bernoulli , 5 : 705 – 719 .
   Web of Science ®Google Scholar
• Lindsay , B. G. 1989 . Moment matrices: Applications in mixtures . Annals of Statistics , 17 : 722 – 740 .
   Web of Science ®Google Scholar
• Lindsay , B. G. 1995 . Mixture Models: Theory, Geometry and Applications , Hayward : Institute for Mathematical Statistics .
   Google Scholar
• McLachlan , G. J. and Peel , D. 2000 . Finite Mixture Models , New York : Wiley .
   Google Scholar
• Morris , C. N. 1982 . Natural exponential families with quadratic variance functions . Annals of Statistics , 10 : 65 – 80 .
   Web of Science ®Google Scholar
• Morris , C. N. 1983 . Natural exponential families with quadratic variance functions: Statistical theory . Annals of Statistics , 11 : 515 – 529 .
   Web of Science ®Google Scholar
• Ning , W. , Gupta , A. K. , Yu , C. and Zhang , S. G. 2009a . A moment-based test for the homogeneity in finite mixture models . Communications in Statistics-Theory and Methods , 38 : 1371 – 1382 .
   Web of Science ®Google Scholar
• Ning , W. , Zhang , S. G. and Yu , C. 2009b . A moment-based test for the homogeneity in mixture natural exponential family with quadratic variance functions . Statistical and Probability Letters , 79 : 828 – 834 .
   Google Scholar
• Shoukri , M. and Lathrop , G. M. 1993 . Statistical testing of genetic linkage under heterogeneity . Biometrics , 49 : 151 – 161 .
   PubMed Web of Science ®Google Scholar
• Smith , C. A. B. 1963 . Testing for heterogeneity of recombination fraction values in human genetics . Annals of Human Genetics , 27 : 175 – 182 .
   PubMed Web of Science ®Google Scholar
• Thode , H. C. , Finch , S. J. and Mendell , M. R. 1988 . Simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals . Biometrics , 44 : 1195 – 1201 .
   PubMed Web of Science ®Google Scholar
• Titterington , D. M. , Smith , A. F. M. and Makov , U. E. 1985 . Statistical Analysis of Finite Mixture Distributions , New York : Wiley .
   Google Scholar
• Wu , Y. and Gupta , A. K. 2003 . Local score tests in mixture exponential family . Journal of Statistical Planning and Inference , 116 : 421 – 435 .
   Web of Science ®Google Scholar