Consider a finite population $u$, which can be viewed as a realization of a superpopulation model. A simple ratio model (linear regression, without intercept) with heteroscedastic errors is supposed to have generated u. A random sample is drawn without replacement from $u$. In this set-up a two-stage wild bootstrap resampling scheme as well as several other useful forms of bootstrapping in finite populations will be considered. Some asymptotic results for various bootstrap approximations for normalized and Studentized versions of the well-known ratio and regression estimator are given. Bootstrap based confidence intervals for the population total and for the regression parameter of the underlying ratio model are also discussed.

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CWI
Department of Operations Research, Statistics, and System Theory [BS]

Helmers, R, & Wegkamp, M.H. (1995). Wild bootstrapping in finite populations with auxiliary information. Department of Operations Research, Statistics, and System Theory [BS]. CWI.