Abstract: The bootstrap approach to model
based inference was first proposed by Chambers and Dorfman [1]. Ouma and Wafula
[7] re-looked at the conditions and extended this work. However, both cases
focused on simple random sampling in cases where the auxiliary variables are
known for the entire population. Our contribution is that we now present a
bootstrap approach to the same kind of inference in two stage cluster sampling
with unequal cluster sizes. Similar work has been done by Kelly and
Cumberland
[6], Bjørnstad and Ytterstad [5]. Unlike them, however, we consider a case in
which the cluster sizes are known only for the sampled clusters, and we make use
of the population model arising from the variance component of the auxiliary
variables to provide a consistent estimator
for the population total. We also choose our initial sampling weights
differently as an attempt to address the gaps that emerged from their use of the
weights due to Rao and Wu [8]. Our proposed model is unbiased for the population
total. The asymptotic behaviour of the error term in our proposed model may also
be used to explain the choice of a sampling scheme in which the cluster sizes
are fixed.
Keywords and phrases: model based surveys, two stage sampling.
