Browse > Article
http://dx.doi.org/10.5351/KJAS.2016.29.3.513

An approximate fitting for mixture of multivariate skew normal distribution via EM algorithm  

Kim, Seung-Gu (Department of Data and Information, Sangji University)
Publication Information
The Korean Journal of Applied Statistics / v.29, no.3, 2016 , pp. 513-523 More about this Journal
Abstract
Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.
Keywords
multivariate skew normal distribution; mixture model; EM algorithm; multivariate normal cdf;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Azzalini, A. (1985). A class of distribution which includes the normal ones, Scandinavian Journal of Statistics, 33, 561-574.
2 Azzalini, A. and Dalla-Valle, A. (1996). The multivariate skew normal distribution, Biometrika, 83, 715-726.   DOI
3 Arellano-Valle, R. B. and Genton, M. G. (2005). On fundamental skew distributions, Journal of Multivariate Analysis, 96, 93-116.   DOI
4 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
5 Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, Wiley, New York.
6 Ho, H. J., Lin, T. I., Chen, H.-Y., and Wang, W.-L. (2012). Some results on the truncated multivariate t distribution, Journal of Statistical Planning & Inference, 142, 25-40.   DOI
7 Kim, S.-G. (2014). An alternating approach of maximum likelihood estimation for mixture of multivariate skew t-distribution, The Korean Journal of Applied Statistics, 27, 819-831.   DOI
8 Lee, S. X. and McLachlan, G. J. (2013). On mixtures of skew normal and skew t-distributions, Advances in Data Analysis and Classification, 7, 241-266.   DOI
9 Lee, S. X. and McLachlan, G. J. (2014a). Finite mixtures of multivariate skew t-distributions: some recent and new results, Statistics and Computing, 24, 181-202.   DOI
10 Lee, S. X. and McLachlan, G. J. (2014b). Finite mixtures of canonical fundamental skew t-distributions, arXiv: 1405.0685v1 [Stat. ME] 4 May 2014.
11 Lin, T.-I. (2010). Robust mixture modeling using multivariate skew t-distributions, Statistics and Computing, 20, 343-356.   DOI
12 Olson, J. M. and Weissfeld, L. A. (1991). Approximation of certain multivariate integrals, Statistics & Probability Letters, 11, 309-317.   DOI
13 Pyne, S., Hu, X., Wang, K., Rossin, E., Lin, T. I., Maier, L., Baecher-Allan, C., McLachlan, G. J., Tamayo, P., Hafler, D. A., De Jager, P. L., and Mesirov, J. P. (2009). Automated high-dimensional flow cytometric data analysis, In Proceedings of the National Academy of Sciences, 106 , 8519-8524.   DOI
14 Sahu, S. K., Dey, D. K., and Branco, M. D. (2003). A new class of multivariate skew distribution with application to Bayesian regression model, The Canadian Journal of Statistics, 31, 129-150.   DOI