International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 571-582

A note on sufficiency in coherent models

D. Basu1 and S. C. Cheng2

1Department of Statistics, Florida State University, Tallahassee 32306, Florida, USA
2Math Department, Creighton University, Omaha 68178, Nebraska, USA

Received 18 February 1980

Copyright © 1981 D. Basu and S. C. Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Partly of an expository nature, this article brings together a number of notions related to sufficiency in an abstract measure theoretic setting. The notion of a coherent statistical model, as introduced by Hasegawa and Perlman [6], is studied in some details. A few results are generalized and their earlier proofs simplified. Among other things, it is shown that a coherent model can be connected in the sense of Basu [2] if and only if no splitting set (Koehn and Thomas, [7]) exists.