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

In: Mathematical Statistics and Probability Theory

Author

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  • György Michaletzky

    (Loránd Eötvös University, Dept. of Probability Theory)

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.

Suggested Citation

  • György Michaletzky, 1987. "On the σ-Fields Which are Larger than a Sufficient One," Springer Books, in: M. L. Puri & P. Révész & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 231-236, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3963-9_17
    DOI: 10.1007/978-94-009-3963-9_17
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