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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 641-653

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\centerline{\large\bf EFFICIENT REPLICATION VARIANCE ESTIMATION}
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\centerline{\large\bf FOR TWO-PHASE SAMPLING}
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\author{J. K. Kim and R. R.  Sitter}
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\centerline{\it Hankuk University of Foreign Studies and Simon Fraser
University}
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\begin{quotation}
\noindent {\it Abstract:}
Variance estimation for the
regression estimator  for a two-phase sample is investigated. A
replication variance estimator with number of replicates equal to
or slightly larger than the size of the second-phase sample is
developed. In surveys where the second-phase sample is much
smaller than the first-phase sample, the procedure has practical
advantages. The method is similar in spirit to one of
Fuller (1998), but is more easily applied and avoids some of that
method's difficulties. The proposed method can be
directly applied to variance estimation for the double expansion
estimator and the reweighted expansion estimator. In these cases,
the proposed method is asymptotically equivalent to the full
jackknife, but uses a smaller number of replications.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Double sampling, jackknife, regression estimator.\par
\end{quotation}
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