Inference of population total in two stage cluster sampling with unequal cluster sizes Academic Article uri icon


  • 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], Bj�rnstad 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.

publication date

  • 2010


  • model based surveys
  • two stage sampling

number of pages

  • 15

start page

  • 182

end page

  • 197


  • 2


  • 2