Multiterminal estimation theory

Abstract

The basic questions here are how to construct effective encoders @,Q2 and the related estimators 6 for the parameter 0; what is the minimum variance of these estimators ?; and what is the maximum Fisher information attainable under the rate constraints RI .R2 for the Shannon information ?. etc. We shall give several substantial answers to these problems which include as special cases the previous results by Zhang and Berger, and by Ahlswede and Burnashev. The present results have been established technically on the basis of universal coding for relevant auxiliary random variables, projection operation for multivariate Gaussian statistics, introduction of a dual pair of orthogonal coordinate systems, and also geometry of Kullback-Leibler's divergences, etc. Such an approach is essentially along the differential-geometrical standpoint provided by Amari in studying the zero-rate estimators. Our estimators can be regarded as a kind of the generalized maximum-likelihood estimators of invariant form under parameter transformations, and are very naturally extended to the multi-parameter case, in contrast with those previously known estimators. As a by-product, we shall show a simple new proof to the result by Zhang and Berger, which enables us to have a clearer understanding for the additivity condition assumed by them.