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\footnotesize
\noindent Statistica Sinica {\bf 11}(2001), 147-172
\vspace{3pc} \normalsize

\centerline{\large\bf ESTIMATORS FOR THE LINEAR REGRESSION MODEL}
\vspace{2pt}
\centerline{\large\bf BASED ON WINSORIZED OBSERVATIONS}
\vspace{.25cm}
\centerline{L-A Chen, A. H. Welsh and W. Chan}
\vspace{.4cm}
\centerline{\it National Chiao Tung University, Australian National University}
\vspace{.2cm}
\centerline{\it and University of Texas-Houston}
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\begin{quotation}
\noindent {\it Abstract:}
We develop an asymptotic, robust version
of the Gauss-Markov theorem for estimating
the regression parameter vector $\beta$ and a parametric
function $c'\beta$ in the linear regression model. In a class of estimators for
estimating
$\beta$ that are linear
in a Winsorized observation
vector introduced by Welsh (1987), we show that
Welsh$'$s trimmed mean has smallest asymptotic covariance matrix.
Also, for estimating a parametric function
$c'\beta$,
the inner product of $c$ and the trimmed mean has the
smallest asymptotic variance among a class of estimators
linear in the Winsorized observation vector.
A generalization of the linear Winsorized mean to
the multivariate context is also given. Examples
analyzing American lobster data and the mineral content of bones
are used to compare the
robustness of some trimmed mean methods.\par
\vspace{9pt} \noindent {\it Key words and phrases:}
Linear regression, robust estimation, trimmed mean, Winsorized mean. \par
\end{quotation}
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