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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 1103-1121

\footnotesize \noindent

\vspace{3pc} \normalsize \centerline{\large\bf SEMIPARAMETRIC PSEUDO
LIKELIHOODS FOR} \vspace{2pt} \centerline{\large\bf LONGITUDINAL
DATA WITH OUTCOME-DEPENDENT} \vspace{2pt} \centerline{\large\bf
NONMONOTONE NONRESPONSE} \vspace{.25cm}

\author{Deyuan Jiang and Jun Shao}
\vspace{.4cm} \centerline{\it University of Wisconsin and East China
Normal University} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} In a study with longitudinal outcomes, the
outcome nonresponse mechanism often depends on the observed or
unobserved value of the outcome. When nonresponse is monotone in the
sense that a subject having a missing outcome at time $t$ is not
observed after time $t$, %\cite{10}
Tang, Little, and Raghunathan (2003)
 developed a semiparametric pseudo-likelihood method for the
estimation of parameters of interest. In practice, however,
nonresponse is often not monotone and a direct application of their
method discards observed data from subjects having nonmonotone
nonresponse, which may result in inefficient estimators. We extend
the idea in %\cite{10}
Tang et al.\ (2003)
to nonmonotone nonresponse and construct a semiparametric
pseudo-likelihood that utilizes all observed data. Asymptotic
normality of the maximum pseudo-likelihood estimators is
established. An application is made to the household income data
from the Health and Retirement Study. Simulation results are also
presented to examine finite sample properties of the proposed
estimators.\par \vspace{9pt} \noindent {\it Key words and phrases:}
Efficiency, nonignorable missing, semiparametric likelihood,
sequential estimation. \par
\end{quotation}

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