The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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An Alternating Approach of Maximum Likelihood Estimation for Mixture of Multivariate Skew t-Distribution

치우친 다변량 t-분포 혼합모형에 대한 최우추정

  • Kim, Seung-Gu (Department of Data and Information, Sangji University)
  • 김승구 (상지대학교 데이터정보학과)
  • Received : 2014.09.01
  • Accepted : 2014.09.22
  • Published : 2014.10.31
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Abstract

The Exact-EM algorithm can conventionally fit a mixture of multivariate skew distribution. However, it suffers from highly expensive computational costs to calculate the moments of multivariate truncated t-distribution in E-step. This paper proposes a new SPU-EM method that adopts the AECM algorithm principle proposed by Meng and van Dyk (1997)'s to circumvent the multi-dimensionality of the moments. This method offers a shorter execution time than a conventional Exact-EM algorithm. Some experments are provided to show its effectiveness.

치우친 다변량 t-분포 혼합을 적합하기 위해 Exact-EM 알고리즘이 사용된다. 그러나 이 방법은 E-step에서 매우 긴 처리시간을 요하는 다변량 절단 t-분포의 적률을 계산해야 한다. 본 논문에서는 이러한 문제점을 완화하기 위해 SPU-EM이라 명명한 알고리즘을 제안하는데, 이것은 Meng과 van Dyk (1997)의 AECM 알고리즘의 원리를 이용하여 다차원 적률의 계산상의 어려움을 해결한다. 결과적으로 제안된 방법은 Exact-EM 알고리즘 보다 빠른 처리시간으로 보장한다. 이를 입증하기 위해 실험을 통해 제안된 방법의 유효성을 보인다.

Keywords

References

  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. https://doi.org/10.1093/biomet/83.4.715
  3. Arellano-Valle, R. B. and Genton, M. G. (2005) On fundamental skew distributions, Journal of Multivariate Analysis, 96, 93-116. https://doi.org/10.1016/j.jmva.2004.10.002
  4. Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, 56, Wiley, New York.
  5. 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. https://doi.org/10.1016/j.jspi.2011.06.006
  6. Kim, S. G. (2012). Diagnosis of observations after fit of multivariate skew t-distribution: Identification of outliers and edge observations from asymmetric Data, The Korean Journal of Applied Statistics, 25, 1019-1026. https://doi.org/10.5351/KJAS.2012.25.6.1019
  7. 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. https://doi.org/10.1007/s11634-013-0132-8
  8. 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. https://doi.org/10.1007/s11222-012-9362-4
  9. Lee, S. X. and McLachlan G. J. (2014b). Finite mixtures of canonical fundamental skew t-distributions, arXiv: 1405.0685v1 [Stat. ME] 4 May 2014.
  10. Lin, T. I. (2010). Robust mixture modeling using multivariate skew t-distributions, Statistics and Computing, 20, 343-356. https://doi.org/10.1007/s11222-009-9128-9
  11. Meng. X. L, and van Dyk, D. A. (1997). The EM-algorithm and old folk song sung to a fast new tune, Journal of the Royal Statistical Society B, 59, 511-567. https://doi.org/10.1111/1467-9868.00082
  12. Pyne, S., Hu, X., Wang, K., Rossin, E., Lin, T. I., Maier, L., Baecher-Allan, C., McLachlan, G. J., Tamayo, P., Ha er, D. A., De Jager, P. L. and Mesirov, J. P. (2009). Automated high-dimensional flow cytometric data analysis, Proc. Natl. Acad. Sci. USA, 106, 8519-8524. https://doi.org/10.1073/pnas.0903028106
  13. 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. https://doi.org/10.2307/3316064

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