Minimax strategies in survey sampling

Gabler, Siegfried ; Stenger, Horst

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URN: urn:nbn:de:bsz:180-madoc-10396
Document Type: Working paper
Year of publication: 1999
The title of a journal, publication series: Discussion Papers / Institut für Volkswirtschaftslehre und Statistik
Volume: 572
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > Sonstige - Fakultät für Rechtswissenschaft und Volkswirtschaftslehre
MADOC publication series: Institut für Volkswirtschaftslehre und Statistik > Discussion Papers
Subject: 330 Economics
Subject headings (SWD): Minimaxlösung , Risiko
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.
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