Statistica Sinica 16(2006), 7-14

A NOTE ON MINIMAL SUFFICIENCY

J. E. Chacón, J. Montanero, A. G. Nogales and P. Pérez

Universidad de Extremadura

Abstract: 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 in Hall, Wijsman and Ghosh (1965).

Key words and phrases: Completeness, invariance, minimal sufficiency.