An effective method for selecting the number of components in density mixtures

References

• Redner , R. A. and Walker , H. F. 1984 . Mixture densities, maximum likelihood and the EM algorithm . SIAM Review , 26 : 195 – 239 .
   Web of Science ®Google Scholar
• Derin , H. 1987 . Estimating components of univariate gaussian mixtures using Prony's method . IEEE Transactions on Pattern Analysis and Machine Intelligence , 9 : 142 – 148 .
   PubMedGoogle Scholar
• Tadjudin , S. and Landgrebe , D. A. 2000 . Robust parameter estimation for mixture model . IEEE Transactions on Geoscience and Remote Sensing , 38 : 439 – 445 .
   Web of Science ®Google Scholar
• Titterington , D. M. , Smith , A. F.M. and Makov , U. E. 1985 . Statistical Analysis of Finite Mixture Distributions , Chichester : John Wiley & Sons Ltd. .
   Google Scholar
• McLachlan , G. and Basford , K. 1988 . Mixture Models: Inference and Applications to Clustering , New York : Marcel Dekker .
   Google Scholar
• Windham , M. P. and Cutler , A. 1992 . Information ratios for validating mixture analyses . Journal of the American Statistical Association , 87 : 1188 – 1192 .
   Web of Science ®Google Scholar
• Crawford , S. 1994 . An application of the laplace method to finite mixture distributions . Journal of the American Statistical Association , 89 : 259 – 267 .
   Web of Science ®Google Scholar
• Feng , Z. D. and McCulloch , C. E. 1996 . Using bootstrap likelihood ratios in finite mixture models . Journal of the Royal Statistical Society Series B , 58 : 609 – 617 .
   Google Scholar
• Polymenis , A. and Titterington , D. M. 1998 . On the determination of the number of components in a mixture . Statistics and Probability Letters , 38 : 295 – 298 .
   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
• Chen , J. and Kalbfleisch , J. D. 1996 . Penalized minimum-distance estimates in finite mixture models . Canadian Journal of Statistics , 24 : 167 – 175 .
   Web of Science ®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
• Escobar , M. D. and West , M. 1995 . Bayesian density estimation and inference using mixtures . Journal of the American Statistical Association , 90 : 577 – 588 .
   Web of Science ®Google Scholar
• Richardson , S. and Green , P. 1997 . On Bayesian analysis of mixtures with an unknown number of components . Journal of the Royal Statistical Society Series B , 59 : 731 – 758 .
   Google Scholar
• Roeder , K. and Wasserman , L. 1997 . Practical bayesian density estimation using mixtures of normals . Journal of the American Statistical Association , 92 : 894 – 902 .
   Web of Science ®Google Scholar
• Efron , B. and Tibshirani , R. J. 1993 . An Introduction to the Bootstrap , New York : Champman and Hall .
   Google Scholar
• Jones , M. C. , Marron , J. S. and Sheather , S. J. 1996 . A brief survey of bandwidth selection for density estimation . Journal of the American Statistical Association , 91 : 401 – 407 .
   Web of Science ®Google Scholar
• Wand , M. P. and Gutierrez , R. G. 1997 . Exact risk approaches to smoothing parameter selection . Journal of Nonparametric Statistics , 8 : 337 – 354 .
   Google Scholar
• Lee , T. C.M. 2001 . A stabilized bandwidth selection method for kernel smoothing of the periodogram . Signal Processing , 81 : 419 – 430 .
   Web of Science ®Google Scholar
• Schwarz , G. 1978 . Estimating the dimension of a model . The Annals of Statistics , 6 : 461 – 464 .
   Web of Science ®Google Scholar
• Rissanen , J. 1989 . Stochastic Complexity in Statistical Inquiry , Singapore : World Scientific .
   Google Scholar
• Keribin , C. 2000 . Consistent estimation of the order of mixture models . Sankhya , 62 : 49 – 66 .
   Google Scholar