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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 1639-1660

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.282

\vspace{3pc} \normalsize \centerline{\large\bf OUTLIER DETECTION AND
TRIMMED ESTIMATION} \vspace{2pt} \centerline{\large\bf  FOR GENERAL
FUNCTIONAL DATA} \vspace{.25cm}
\author{Daniel Gervini}
\vspace{.4cm} \centerline{\it University of Wisconsin--Milwaukee}
\vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} This article introduces trimmed estimators
for the mean and covariance function of general functional data. The
estimators are based on a new measure of ``outlyingness'' or data
depth\ that is well defined on any metric space, although we focus
on Euclidean spaces. We compute the breakdown point of the
estimators and show that the optimal breakdown point is attainable
for the appropriate choice of tuning parameters. The small-sample
behavior of the estimators is studied by simulation, and we show
that they have better outlier-resistance properties than alternative
estimators. This is confirmed by two data applications that also
show that the outlyingness measure can be used as a graphical
outlier-detection tool in functional spaces where visual screening
of the data is difficult.\par \vspace{9pt} \noindent {\it Key words
and phrases:} Breakdown point, data depth, robust statistics,
stochastic processes. \par
\end{quotation}
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