Minimal Sufficient $|sigma$-Fields and Minimal Sufficient Statistics. Two Counterexamples
Dieter Landers, Lothar Rogge · The Annals of Mathematical Statistics · 1972
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.