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\noindent Statistica Sinica {\bf 13}(2003), 613-623

\vspace{3pc} \normalsize
\centerline{\large\bf TWO-WAY CONTINGENCY TABLES UNDER}
\vspace{2pt}
\centerline{\large\bf CONDITIONAL HOT DECK IMPUTATION}
\vspace{.25cm}
\author{Hansheng Wang and Jun Shao}
\vspace{.4cm}
\centerline{\it Peking University and University of Wisconsin}
\vspace{.55cm}

\begin{quotation}
\noindent {\it Abstract:}
We consider the estimation of cell probabilities
in a two-way contingency table where
the two-dimensional categorical data have nonrespondents
imputed by using a conditional hot deck imputation method.
Under simple random sampling, we establish asymptotic normality
of cell probability  estimators  based on imputed data and derive
explicitly the form of their asymptotic covariance matrix, which
can be used for
large sample inference. We also show that estimators based on imputed data
are more efficient than those obtained by ignoring nonrespondents
and re-weighting when the proportion of nonrespondents is large.
The results are extended to stratified sampling, under imputation,
within each stratum or across strata. Two types of asymptotics are
studied under stratified sampling. One deals with the case of a fixed number
of strata with large stratum sizes and the other deals
with the situation of a large number of strata with small stratum sizes.
Some simulation results are presented to study finite sample
properties of the proposed procedures.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Estimation of cell probability, imputation across strata,
re-weighting, stratified sampling.\par
\end{quotation}
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