Resampling Methods for Sample Surveys

by Brett Presnell and James G. Booth

Abstract:

Application of the bootstrap in sample survey settings presents
considerable practical and conceptual difficulties and various
potential solutions have recently been proffered in the statistical
literature.  This paper provides a critical review of these methods
along with a new method which does not seem to have appeared in the
literature although it is closely related to a method based on a
plug-in rule for without replacement sampling proposed by Booth,
Butler, and Hall (1994).  Use of these various methods to construct
bootstrap percentile-$t$ confidence intervals is discussed from the
point of view of first-order asymptotic accuracy, correcting several
errors and omissions in the literature.  Some open questions
concerning second-order asymptotics are also answered, and results are
provided from a small simulation study supporting the major points of
the paper.

Two of the methods discussed can be justified as plug-in rules, and
thus have a fairly straightforward motivation.  In comparison the
others methods appear ad hoc and overly complex.  While further
empirical study is needed, practical considerations, asymptotic
theory, and the empirical evidence thus far available indicate that
for confidence interval construction the methods based on a plug-in
rule are preferable to other available methods.
 
Keywords:  Bootstrap, confidence interval, Edgeworth expansion, finite
           population, resampling, second-order correct, survey data.