Published in Viswanathan, R. (1993). A note on distributed estimation and sufficiency. IEEE Transactions on Information Theory, 39(5), 1765 - 1767. doi: 10.1109/18.259674 ©1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.


In relation to distributed parameter estimation, the notion of local and global sufficient statistics is introduced. It is shown that when a sufficiency condition is satisfied by the probability distribution of a random sample, a global sufficient statistic is obtainable as a function of local sufficient statistics. Several standard distributions satisfy the said sufficiency condition.