Open Access
April, 1972 A Note on Sufficiency and Invariance
Robert H. Berk
Ann. Math. Statist. 43(2): 647-650 (April, 1972). DOI: 10.1214/aoms/1177692645


Under certain conditions, it is shown that the invariant and almost-invariant $\sigma$-fields are equivalent if and only if the invariant $\sigma$-field is independent of an appropriate sufficient $\sigma$-field. This result helps unify work of Hall, Wijsman and Ghosh and of Pfanzagl, who dealt with the forward implication and work of Berk and Bickel, who treated the reverse implication. The conditions required are that the sufficient and invariant $\sigma$-fields be essentially disjoint and together generate the $\sigma$-field of the original data.


Download Citation

Robert H. Berk. "A Note on Sufficiency and Invariance." Ann. Math. Statist. 43 (2) 647 - 650, April, 1972.


Published: April, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0254.62002
MathSciNet: MR298810
Digital Object Identifier: 10.1214/aoms/1177692645

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 2 • April, 1972
Back to Top