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Pair-perturbation influence functions of nongaussianity by projection pursuit

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  • Huang, Yufen
  • Cheng, Ching-Ren
  • Wang, Tai-Ho

Abstract

The most nongaussian direction to explore the clustering structure of the data is considered to be the interesting linear projection direction by applying projection pursuit. Nongaussianity is often measured by kurtosis, however, kurtosis is well known to be sensitive to influential points/outliers and the projection direction is essentially affected by unusual points. Hence in this paper we focus on developing the influence functions of projection directions to investigate the influence of abnormal observations especially on the pair-perturbation influence functions to uncover the masked unusual observations. A technique is proposed for defining and calculating influence functions for statistical functional of the multivariate distribution. A simulation study and a real data example are provided to illustrate the applications of these approaches.

Suggested Citation

  • Huang, Yufen & Cheng, Ching-Ren & Wang, Tai-Ho, 2008. "Pair-perturbation influence functions of nongaussianity by projection pursuit," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3971-3987, April.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:8:p:3971-3987
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    References listed on IDEAS

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    1. Huang, Yufen & Kuo, Mei-Ling & Wang, Tai-Ho, 2007. "Pair-perturbation influence functions and local influence in PCA," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5886-5899, August.
    2. He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
    3. Fung, Wing-Kam, 1992. "Some diagnostic measures in discriminant analysis," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 279-285, March.
    4. Huang, Yufen & Kao, Tzu-Ling & Wang, Tai-Ho, 2007. "Influence functions and local influence in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3844-3861, May.
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