Pair-perturbation influence functions of nongaussianity by projection pursuit

Authors:
Yufen Huang;Ching-Ren Cheng;Tai-Ho Wang
Affiliations:
Department of Mathematics, National Chung Cheng University, Chia-yi 621, Taiwan;Department of Mathematics, National Chung Cheng University, Chia-yi 621, Taiwan;Department of Mathematics, National Chung Cheng University, Chia-yi 621, Taiwan
Venue:
Computational Statistics & Data Analysis
Year:
2008

Citing 5
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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.