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A note on minimal sufficiency. (English) Zbl 1087.62005

Summary: This paper shows that the classes of sufficient and minimal sufficient \(\sigma\)-fields are closed under products. The results are used to construct several examples that throw some light on the study of the relationship between minimal sufficiency and invariance, a problem posed by W. J. Hall, R. A. Wijsman and J. K. Ghosh [Ann. Math. Stat. 36, 575–614 (1965; Zbl 0227.62007)].

MSC:

62B05 Sufficient statistics and fields

Citations:

Zbl 0227.62007
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