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Measurable supports, reducible spaces and the structure of the optimal σ-field in unbiased estimation

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Abstract

This paper generalizes a result bySapozhnikov relating the structure of the optimal σ-field in unbiased estimation to the reducibility of certain linear subspaces of estimators. For this purpose, the concept of a measurable support of (uncountably infinite) sets consisting of random variables is introduced, which could be of general interest. It turns out, that for a wide class of measure spaces, measurable supports of any subsets of measurable functions exist.

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  1. Institut für Statistik und informatik, Universität Wien, Rathausstrasse 19/3, A-1010, Wien, Austria

    Immanuel M. Bomze

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  1. Immanuel M. Bomze
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Bomze, I.M. Measurable supports, reducible spaces and the structure of the optimal σ-field in unbiased estimation. Monatshefte für Mathematik 101, 27–38 (1986). https://doi.org/10.1007/BF01326844

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  • DOI: https://doi.org/10.1007/BF01326844

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