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Chambers and Dorfman (2002) constructed bootstrap confidence intervals in model based estimation for finite population totals assuming that auxiliary values are available throughout a target population and that the auxiliary values are independent. They also assumed that the cluster sizes are known throughout the target population. We now extend to two stage sampling in which the cluster sizes are known only for the sampled clusters, and we therefore predict the unobserved part of the population total. Jan and Elinor (2008) have done similar work, but unlike them, we use a general model, in which the auxiliary values are not necessarily independent. We demonstrate that the asymptotic properties of our proposed estimator and its coverage rates are better than those constructed under the model assisted local polynomial regression model.
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