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Minimax strategies in survey sampling

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  • Gabler, Siegfried
  • Stenger, Horst

Abstract

The risk of a sampling strategy is a function on the parameter space, which is the set of all vectors composed of possible values of the variable of interest. It seems natural to ask for a minimax strategy, minimizing the maximal risk. So far answers have been provided for completely symmetric parameter spaces. Results available for more general spaces refer to sample size 1 or to large sample sizes allowing for asymptotic approximation. In the present paper we consider arbitrary sample sizes, derive a lower bound for the maximal risk under very weak conditions and obtain minimax strategies for a large class of parameter spaces. Our results do not apply to parameter spaces with strong deviations from symmetry. For such spaces a minimax strategy will prescribe to consider only a small number of samples and takes a non-random and purposive character.

Suggested Citation

  • Gabler, Siegfried & Stenger, Horst, 1999. "Minimax strategies in survey sampling," Discussion Papers 572, Institut fuer Volkswirtschaftslehre und Statistik, Abteilung fuer Volkswirtschaftslehre.
    • Handle: RePEc:mnh:vpaper:1039
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    File URL: https://madoc.bib.uni-mannheim.de/1039/1/572.pdf
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    References listed on IDEAS

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    1. S. Gabler & R. Schweigkoffer, 1990. "The existence of sampling designs with preassigned inclusion probabilities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 87-96, December.
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