On the σ-Fields Which are Larger than a Sufficient One

György Michaletzky
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György Michaletzky: Loránd Eötvös University, Dept. of Probability Theory

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 231-236 from Springer

Abstract: Abstract One of the most peculiar features of the set of sufficient σ-fields in a statistical space (Ω, A, P) is that it may happen that a σ-field which is larger than a sufficient one does not remain to be sufficient. In [4] there is a sufficient condition to avoid this pathological nature. According to [4] if the Boolean algebra A/N (P) is complete and F⊂A is a sufficient σ-field, then every σ-field G⊃F for which G/N (P) is a complete subalgebra of A/N (P) is sufficient. In this paper we give a necessary and sufficient condition for that any σ-field containing a fixed sufficient σ-field should be sufficient.

Keywords: Statistical Space; Equivalence Class; Conditional Probability; Boolean Algebra; Peculiar Feature (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_17

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DOI: 10.1007/978-94-009-3963-9_17

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