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Influence analysis of non-Gaussianity by applying projection pursuit

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

Abstract

The Gaussian distribution is the least structured from the information-theoretic point of view. In this paper, projection pursuit is used to find non-Gaussian projections to explore the clustering structure of the data. We use kurtosis as a measure of non-Gaussianity to find the projection directions. Kurtosis is well known to be sensitive to influential points/outliers, and so the projection direction will be greatly affected by unusual points. We also develop the influence functions of projection directions to investigate abnormal observations. A data example illustrates the application of these approaches.

Suggested Citation

  • Huang, Yufen & Cheng, Ching-Ren & Wang, Tai-Ho, 2007. "Influence analysis of non-Gaussianity by applying projection pursuit," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1515-1521, August.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:14:p:1515-1521
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. Huang, Yufen & Wang, Sheng-Wen, 2013. "Influence analysis on the direction of optimal response," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1287-1299.

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