Influence analysis of non-Gaussianity by applying projection pursuit

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.