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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1713-1733

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.070

\vspace{3pc} \normalsize \centerline{\large\bf SENSITIVITY ANALYSIS
OF NONGAUSSIANITY} \vspace{2pt} \centerline{\large\bf  BY PROJECTION
PURSUIT} \vspace{.25cm}
\author{Yufen Huang$^1$, Ching-Ren Cheng$^1$ and Tai-Ho Wang$^2$}
\vspace{.4cm} \centerline{\it $^1$National Chung Cheng
 University and
$^2$Baruch College, CUNY} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} From the information-theoretic point of
view, the Gaussian distribution is the least
  structured.  Therefore, the most non-Gaussian direction in which to explore the clustering structure
of data is considered to be the most interesting linear projection
direction when applying projection pursuit. Non-Gaussianity is often
measured by kurtosis.  However, kurtosis is well-known to be
sensitive to influential points/outliers and
 so the projection direction can be unduly affected by abnormal points.  In
this paper, we focus on developing influence functions of projection
directions in order to detect abnormal observations, especially on
high-dimensional data.  For multivariate data, a new technique is
proposed for defining and developing influence
 functions of projection directions.  In addition, a new influence
 function is suggested.  Two simulated data examples and one concrete data example are
 provided for illustration.\par
\vspace{9pt} \noindent {\it Key words and phrases:} Influence
function,
 kurtosis, non-gaussianity, projection pursuit.\par
\end{quotation}

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