Survey sampling : a linear game

Stenger, Horst ; Gabler, Siegfried ; Schmidt, Jochen

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URN: urn:nbn:de:bsz:180-madoc-10252
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: Discussion Papers / Institut für Volkswirtschaftslehre und Statistik
Volume: 586
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): Umfrage , Statistik , Auslese
Abstract: A linear game consists of two subsets of a vector space with a scalar product. The idea is that players 1 and 2 select, independently, elements of the first and second set, respectively. Then, player 2 has to pay to player 1 the value of the scalar product of the selected elements. We will discuss survey sampling within the framework of linear games with the statistician in the role of player 2. The vector space to be considered is the set of all symmetric matrices of order N x N with a scalar product identical with the usual mean squared error. The subset from which the statistician's selection is to be made is neither convex nor compact. Standard results of the theory of linear games have to be modified appropriately. The existence of minimax strategies will be established. At the same time we hope to improve our understanding of random selection and of the duality between the fixed population approach and model based approaches to the theory of survey sampling.
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