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Gaussian distribution is the least structured from the
information-theoretic point of view. In this thesis, the projection
pursuit is performed by finding the most nongaussian projection to
explore the clustering structure of the data. We use kurtosis as a
measure of nongaussianity to find the projection direction. Kurtosis
is well known to be sensitive to abnormal observations, henceforth
the projection direction will be essentially affected by unusual
points. The perturbation theory provides a useful tool in
sensitivity analysis. In this thesis, we develop influence functions
for the projection direction to investigate the influence of unusual
observations. It is well-known that single-perturbation diagnostics
can suffer from the masking effect. Hence we also develop the
pair-perturbation influence functions to detect the masked
influential points and outliers. A simulated data and a specific
data example are provided to illustrate the applications of these
approaches.
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