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Minimax strategies in survey sampling

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Author Info
Gabler, Siegfried
Stenger, Horst (Institut für Volkswirtschaft und Statistik (IVS))
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 arbittrary 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.

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Paper provided by Institut für Volkswirtschaft und Statistik (IVS), University of Mannheim in its series IVS discussion paper series with number 572.

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Handle: RePEc:mea:ivswpa:572

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