Probability Theory and Related Fields

, Volume 70, Issue 1, pp 131–156 | Cite as

Local asymptotic normality of sampling experiments

  • Hartmut Milbrodt
Article

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 L2-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.

Keywords

Sampling Experiment Sampling Plan Inclusion Probability Triangular Array Rejective Sampling 

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Hartmut Milbrodt
    • 1
  1. 1.Mathematik VII der Universität BayreuthBayreuthFederal Republic of Germany

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