Browse > Article
http://dx.doi.org/10.5351/CKSS.2012.19.5.673

ECM Algorithm for Fitting of Mixtures of Multivariate Skew t-Distribution  

Kim, Seung-Gu (Department of Data and Information, Sangji University)
Publication Information
Communications for Statistical Applications and Methods / v.19, no.5, 2012 , pp. 673-683 More about this Journal
Abstract
Cabral et al. (2012) defined a mixture model of multivariate skew t-distributions(STMM), and proposed the use of an ECME algorithm (a variation of a standard EM algorithm) to fit the model. Their estimation by the ECME algorithm is closely related to the estimation of the degree of freedoms in the STMM. With the ECME, their purpose is to escape from the calculation of a conditional expectation that is not provided by a closed form; however, their estimates are quite unstable during the procedure of the ECME algorithm. In this paper, we provide a conditional expectation as a closed form so that it can be easily calculated; in addition, we propose to use the ECM algorithm in order to stably fit the STMM.
Keywords
Multivariate skew t-distribution; mixture model; ECME algorithm; ECM algorithm; estimation of degree of freedom;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Lin, T.-I., Lee, J.-C. and Yen, S. Y. (2007a). Finite mixture modeling using the skew normal distributions, Statistica Sinica, 17, 909-927.
2 Liu, C. and Rubin, D. B. (1994). The ECME algorithm: a simple extension of EM and ECM with fast monotonic convergence, Biometroka, 81, 633-784.   DOI   ScienceOn
3 McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models, Wiley, New York.
4 Sahu, S. K., Dey, D. K. and Branco, M. D. (2003). A new class of multivariate skew distribution with application to Bayesian regression molel, The Canadian Journal of Statistics, 31, 129-150.   DOI   ScienceOn
5 Azzalini, A. (1985). A class of distribution which includes the normal ones, Scandinavian Journal of Statistics, 33, 561-574.
6 Azzalini, A. and Dalla-Valle, A. (1996). The multivariate skew normal distribution, Biometrika, 83, 715-726.   DOI   ScienceOn
7 Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution, Journal of the Royal Statistical Society, series B 65, 367-389.   DOI   ScienceOn
8 Cabral, C. S., Lachos, V. H. and Prates, M. O. (2012). Multivariate mixture modeling using skew-normal independent distribution, Computational Statistics and Data Analysis, 56, 126-142.   DOI   ScienceOn
9 Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, 56, Wiley, New York.
10 Lee, S. and McLachlan, G. J. (2011). On the fitting of mixtures of multivariate skew t-distributions via the EM algorithm, Technical Report of University of Queensland, Available from: http://arxiv.org/PScache/arxiv/pdf/1109/1109.4706v1.pdf.
11 Lin, T.-I. (2010). Robust mixture modeling using multivariate skew t distributions, Statistics and Computing, 20, 343-356.   DOI
12 Lin, T.-I., Lee, J.-C. and Hsieh, W. J. (2007b). Robust mixture modeling using the skew t distributions, Statistics and Computing, 17, 81-92.   DOI