Finite mixture modelling using the skew normal distribution

Statistica Sinica

Volumn 17, Issue 3, 2007, Pages 909-927

  Lin, Tsung I ^a   Lee, Jack C ^b   Yen, Shu Y ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

ECM algorithm; ECME algorithm; Fisher information; Markov chain Monte Carlo; Maximum likelihood estimation; Skew normal mixtures

Indexed keywords

EID: 34249710125     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd Int. Symp. on Information Theory, (Edited by B. N. Petrov and F. Csaki), 267-281. Akademiai Kiado, Budapest.
2. Arnold, B. C., Beaver, R. J., Groeneveld, R. A. and Meeker, W. Q. (1993). The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika 58, 471-488.
3. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.
4. Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica 46, 199-208.
5. Azzalini, A. and Capitaino, A. (1999). Statistical applications of the multivariate skew-normal distribution. J. Roy. Statist. Soc. Ser. B 61, 579-602.
6. Azzalini, A. and Capitaino, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution J. Roy. Statist. Soc. Ser. B 65, 367-389.
7. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715-726.
8. Basord, K. E., Greenway D. R., McLachlan G. J. and Peel D. (1997). Standard errors of fitted means under normal mixture. Comput. Statist. 12, 1-17.
9. Bechtel, Y. C., Bonaiti-Pellieé, C., Poisson, N., Magnette, J. and Bechtel, P. R. (1993). A population and family study of N-acetyltransferase using caffeine urinary metabolites. Clin. Pharm. Therp. 54, 134-141.
10. Brooks, S. P. and Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. J. Comput. Graph. Statist. 7, 434-455.
11. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39, 1-38.
12. Diebolt, J. and Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling. J. Roy. Statist. Soc. Sec. B 56, 363-375.
13. Efron B. and Tibshirani R. (1986). Bootstrap method for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Sci. 1, 54-77.
14. Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90, 577-588.
15. Gelman, A., Robert, G. and Gilks, W. (1996). Efficient Metropolis jumping rules. In Bayesian Statistics 5 (Edited by J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith). Oxford University Press, New York.
16. Gelman A. and Rubin D. B. (1992). Inference from iterative simulation using multiple sequences. Statist, Sci. 7, 457-472.
17. Genton, M. G. (2004). Skew-Elliptical Distributions and Their Applications. Chapman & Hall, New York.
18. Gupta, A. K., González-Farías G. and Domínguez- Monila, J. A. (2004). A multivariate skew normal distribution. J. Multivariate Anal. 89, 181-190.
19. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.
20. Henze, N. (1986). A probabilistic representation of the "skew-normal" distribution. Scand. J. Statist. 13, 271-275.
21. Jones, M. C. and Faddy, M. J. (2003). A skew extension of the t-distribution, with applications. J. Roy. Statist. Soc. Ser. B 65, 159-174.
22. Lin, T. L., Lee, J. C. and Hsieh, W. J. (2007). Robust mixture modeling using the skew t distribution. Statist. Comput. 17, 81-92.
23. Liu, C. H. and Rubin, D. B. (1994). The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika 81, 633-648.
24. Maclean, C. J., Morton, N. E., Elston, R. C. and Yee, S. (1976). Skewness in commingled distributions. Biometrics 32, 695-599.
25. McLachlan, G. J. and Basord, K. E. (1988). Mixture Models: Inference and Application to Clustering. Marcel Dekker, New York.
26. McLachlan, G. J. and Peel D. (2000). Finite Mixture Models. Wiely, New York.
27. Meng, X. L. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80, 267-278.
28. Meng, X. L. (1994). On the global and componentwise rates of convergence of the EM algorithm. Lin. Alg. Applic. 199, 413-425.
29. Richardson, S. and Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components. J. R. Statist. Soc. B 59, 731-792.
30. Roberts, C. and Geisser, S. (1966). A necessary and sufficient condition for the square of a random variable to be gamma. Biometrika 53, 275-278.
31. Sahu, S. K., Dey, D. K. and Branco, M. D. (2003). A new class of multivariate skew distributions with application to Bayesian regression models. Canad. J. Statist. 31, 129-150.
32. Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461-464.
33. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.
34. Stephens, M. (2000). Bayesian analysis of mixture models with an unknown number of components - an alternative to reversible jump methods. Ann. Statist. 28, 40-74.
35. Titterington, D. M., Smith, A. F. M. and Markov, U. E. (1985). Statistical Analysis of Finite Mixture Distributions. Wiely, New York.