Local asymptotic normality of sampling experiments

Summary Following Hájek's and Madow's asymptotic approach to classical survey sampling, a framework for the asymptotic analysis of superpopulation models is proposed. Within this framework weak limit theorems for sequences of experiments obtained by Poisson sampling and Rejective sampling are derived. In particular, it is shown that the sampling experiments are locally asymptotically normal in LeCam's sense, if the underlying superpopulation model is an L ²-generated regression experiment. This result can e.g. be used to produce Horvitz-Thompson-type estimators which are asymptotically efficient median-unbiased estimates of certain functionals of the regression function.