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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1857-1880

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.306

\vspace{3pc} \normalsize \centerline{\large\bf ESTIMATION IN
MULTIVARIATE $\bm t$ LINEAR MIXED} \vspace{2pt}\centerline
{\large\bf MODELS FOR MULTIPLE LONGITUDINAL DATA} \vspace{.25cm}
\author{Wan-Lun
Wang and Tsai-Hung Fan} \vspace{.4cm} \centerline{\it Feng Chia
University and National Central University} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} The multivariate linear mixed model (MLMM)
is a frequently used tool for a joint analysis of more than one
series of longitudinal data. Motivated by a concern of sensitivity
to potential outliers or data with longer-than-normal tails and
possible serial correlation, we develop a robust generalization of
the MLMM that is constructed by using the multivariate $t$
distribution and a parsimonious AR($p$) dependence structure for the
within-subject errors. A score test for the inspection of
autocorrelation among within-subject errors is derived. A hybrid
ECME-scoring procedure is developed for computing the maximum
likelihood estimates with standard errors as a by-product. The
methodology is illustrated through an application to a set of AIDS
data and several simulation studies.\par \vspace{9pt} \noindent {\it
Key words and phrases:} AR($p$), ECME algorithm, outliers, random
effects, score test. \par
\end{quotation}

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