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\footnotesize \noindent Statistica Sinica {\bf 23} (2013), 213-230

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.240

\vspace{3pc} \normalsize \centerline{\large\bf ESTIMATION OF
MULTIVARIATE MEANS WITH} \vspace{2pt} \centerline{\large\bf
HETEROSCEDASTIC ERRORS USING} \vspace{2pt} \centerline{\large\bf
ENVELOPE MODELS} \vspace{.25cm}
\author{Zhihua Su and R. Dennis Cook}
\vspace{.4cm} \centerline{\it University of Florida and University
of Minnesota} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} In this article, we propose envelope
models that accommodate heteroscedastic error structure in the
framework of estimating multivariate means for different
populations.  Envelope models were introduced by Cook, Li, and
Chiaromonte (2010)
 as a parsimonious version of multivariate
linear regression that achieves efficient estimation of the
coefficients by linking the mean function and the covariance
structure.  In the original development, constant covariance
structure was assumed. The heteroscedastic envelope models we
propose are more flexible in allowing a more general covariance
structure.  Their asymptotic variances and Fisher consistency are
studied.  Simulations and data examples show that they are more
efficient than standard methods of estimating the multivariate
means, and also more efficient than the envelope model assuming
constant covariance structure.\par \vspace{9pt} \noindent {\it Key
words and phrases:} Dimension reduction, envelope model, Grassmann
manifold, reducing subspace.
\par
\end{quotation}

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