Inference on the Order of a Normal Mixture

REFERENCES

• Bartlett , M. S. 1953 . “Approximate Confidence Intervals. I,” . Biometrika , 40 : 12 – 19 .
   Web of Science ®Google Scholar
• Benjamini , Y. and Hochberg , Y. 1995 . “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” . Journal of the Royal Statistical Society, Series B , 57 : 289 – 300 .
   Web of Science ®Google Scholar
• Charnigo , R. and Sun , J. 2004 . “Testing Homogeneity in a Mixture Distribution via the L 2-Distance Between Competing Models,” . Journal of the American Statistical Association , 99 : 488 – 498 .
   Web of Science ®Google Scholar
• Chen , H. and Chen , J. 2003 . “Tests for Homogeneity in Normal Mixtures With Presence of a Structural Parameter,” . Statistica Sinica , 13 : 351 – 365 .
   Web of Science ®Google Scholar
• Chen , J. 1995 . “Optimal Rate of Convergence in Finite Mixture Models,” . The Annals of Statistics , 23 : 221 – 234 .
   Web of Science ®Google Scholar
• Chen , J. and Khalili , A. 2008 . “Order Selection in Finite Mixture Models With a Non-Smooth Penalty,” . Journal of the American Statistical Association , 103 : 1674 – 1683 .
   Web of Science ®Google Scholar
• Chen , J. and Li , P. 2009 . “Hypothesis Test for Normal Mixture Models: The EM Approach,” . The Annals of Statistics , 37 : 2523 – 2542 .
   Web of Science ®Google Scholar
• Chen , J. , Tan , X. and Zhang , R. 2008 . “Inference for Normal Mixtures in Mean and Variance,” . Statistica Sinica , 18 : 443 – 465 .
   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
• Dacunha-Castelle , D. and Gassiat , E. 1999 . “Testing the Order of a Model Using Locally Conic Parametrization: Population Mixtures and Stationary ARMA Processes,” . The Annals of Statistics , 27 : 1178 – 1209 .
   Web of Science ®Google Scholar
• Efron , B. 2004 . “Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis,” . Journal of the American Statistical Association , 99 : 96 – 104 .
   Web of Science ®Google Scholar
• Efron , B. 2010 . Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction (Institute of Mathematical Statistics Monographs, Vol. I) , Cambridge : Cambridge University Press .
   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 Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer (Vol. 2) , Edited by: LeCam , L. and Olshen , R. A. 789 – 806 . Monterey, CA : Wadsworth .
   Google Scholar
• Hartigan , J. A. 1985 . “A Failure of Likelihood Asymptotics for Normal Mixtures,” . In Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer (Vol. 2) , Edited by: LeCam , L. and Olshen , R. A. 807 – 810 . Monterey, CA : Wadsworth .
   Google Scholar
• Hathaway , R. J. 1985 . “A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions,” . The Annals of Statistics , 13 : 795 – 800 .
   Web of Science ®Google Scholar
• Ishwaran , H. , James , L. F. and Sun , J. 2001 . “Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions,” . Journal of the American Statistical Association , 96 : 1316 – 1332 .
   Web of Science ®Google Scholar
• James , L. F. , Priebe , C. E. and Marchette , D. J. 2001 . “Consistent Estimation of Mixture Complexity,” . The Annals of Statistics , 29 : 1281 – 1296 .
   Web of Science ®Google Scholar
• Jeffries , N. O. 2003 . “A Note on Testing the Number of Components in a Normal Mixture,” . Biometrika , 90 : 991 – 994 .
   Web of Science ®Google Scholar
• Keribin , C. 2000 . “Consistent Estimation of the Order of Mixture Models,” . Sankhya , 62 : 49 – 66 .
   Google Scholar
• Leroux , B. 1992 . “Consistent Estimation of a Mixture Distribution,” . The Annals of Statistics , 20 : 1350 – 1360 .
   Web of Science ®Google Scholar
• Li , P. and Chen , J. 2010 . “Testing the Order of a Finite Mixture Model,” . Journal of the American Statistical Association , 105 : 1084 – 1092 .
   Web of Science ®Google Scholar
• Liu , X. and Shao , Y. 2003 . “Asymptotics for Likelihood Ratio Tests Under Loss of Identifiability,” . The Annals of Statistics , 31 : 807 – 832 .
   Web of Science ®Google Scholar
• Lo , Y. , Mendell , N. R. and Rubin , D. B. 2001 . “Testing the Number of Components in a Normal Mixture,” . Biometrika , 88 : 767 – 778 .
   Web of Science ®Google Scholar
• Maitra , R. and Melnykov , V. 2010 . “Simulating Data to Study Performance of Finite Mixture Modeling and Model-Based Clustering Algorithms,” . Journal of Computational and Graphical Statistics , 19 : 354 – 376 .
   Web of Science ®Google Scholar
• McLachlan , G. J. 1987 . “On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture,” . Journal of the Royal Statistical Society, Series C , 36 : 318 – 324 .
   Web of Science ®Google Scholar
• McLachlan , G. J. , Bean , R. W. and Ben-Tovim Jones , L. 2006 . “A Simple Implementation of a Normal Mixture Approach to Differential Gene Expression in Multiclass Microarrays,” . Bioinformatics , 22 : 1608 – 1615 .
   PubMed Web of Science ®Google Scholar
• McLachlan , G. J. and Peel , D. 2000 . Finite Mixture Models , New York : Wiley .
   Google Scholar
• Miloslavsky , M. and van der Laan , M. J. 2003 . “Fitting of Mixtures With Unspecified Number of Components Using Cross-Validation Distance Estimate,” . Computational Statistics and Data Analysis , 41 : 413 – 428 .
   Web of Science ®Google Scholar
• Monetti , A. , Versini , G. , Dalpiaz , G. and Reniero , F. 1996 . “Sugar Adulterations Control in Concentrated Rectified Grape Musts by Finite Mixture Distribution Analysis of the Myo- and Scyllo-Inositol Content and the D/H Methyl Ratio of Fermentative Ethanol,” . Journal of Agricultural and Food Chemistry , 44 : 2194 – 2201 .
   Web of Science ®Google Scholar
• Pavlic , M. , Brand , R. and Cummings , S. M. 2001 . “Estimating Probability of Non-Response to Treatment Using Mixture Distributions,” . Statistics in Medicine , 20 : 1739 – 1753 .
   PubMed Web of Science ®Google Scholar
• R Development Core Team . 2008 . R: A Language and Environment for Statistical Computing , Vienna : R Foundation for Statistical Computing. Available at http://www.R-project.org .
   Google Scholar
• Richardson , S. and Green , P. J. 1997 . “On Bayesian Analysis of Mixtures With an Unknown Number of Components,” . Journal of the Royal Statistical Society, Series B , 59 : 731 – 792 .
   Google Scholar
• Roeder , K. 1994 . “A Graphical Technique for Determining the Number of Components in a Mixture of Normals,” . Journal of the American Statistical Association , 89 : 487 – 500 .
   Web of Science ®Google Scholar
• Schork , N. J. , Allison , D. B. and Thiel , B. 1996 . “Mixture Distributions in Human Genetics,” . Statistical Methods in Medical Research , 5 : 155 – 178 .
   PubMedGoogle Scholar
• Singh , D. , Febbo , P. G. , Ross , K. , Jackson , D. G. , Manola , J. , Ladd , C. , Tamayo , P. , Renshaw , A. A. , D’Amico , A. V. , Richie , J. P. , Lander , E. S. , Loda , M. , Kantoff , P. W. , Golub , T. R. and Sellers , W. R. 2002 . “Gene Expression Correlates of Clinical Prostate Cancer Behavior,” . Cancer Cell , 1 : 203 – 209 .
   PubMed Web of Science ®Google Scholar
• Woo , M. and Sriram , T. N. 2006 . “Robust Estimation of Mixture Complexity,” . Journal of the American Statistical Association , 101 : 1475 – 1485 .
   Web of Science ®Google Scholar