Abstract
In this paper there are solved two problems raised by Bahadur (1954) which concern the relation between the existence of a minimal sufficient $\sigma$-field and the existence of a minimal sufficient statistic. Two examples show that the existence of a minimal sufficient $\sigma$-field is neither necessary nor sufficient for the existence of a minimal sufficient statistic.
Citation
Dieter Landers. Lothar Rogge. "Minimal Sufficient $|sigma$-Fields and Minimal Sufficient Statistics. Two Counterexamples." Ann. Math. Statist. 43 (6) 2045 - 2049, December, 1972. https://doi.org/10.1214/aoms/1177690882
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