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Contents of PMS, Vol. 5, Fasc. 1,
pages 153 - 163
 

A CONDITION TO AVOID A PATHOLOGICAL STRUCTURE OF SUFFICIENT s -FIELDS

György Michaletzky

Abstract: Sufficiency is one of the fundamental concepts of mathematical statistic. For a statistical space (_O_, A,P) a s -field is sufficient if - roughly speaking - it contains the same information regarding the measure class P as the whole s -field A. Burkholder has constructed an example where a nonsufficient s -field is larger than a sufficient one. We show that if the Boolean algebra of equivalence classes of events is complete (where two events A, B are said to be equivalent if P (A o B) = 0 for two every measures P (- P ), then a sub-s -field G containing a sufficient sub-s -field F of A is sufficient iff the Boolean algebra of equivalence classes of events belonging to G is complete.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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