Statistical inference under multiterminal data compression

This paper presents a survey of the literature on the information-theoretic problems of statistical inference under multiterminal data compression with rate constraints. Significant emphasis is put on problems: 1) multiterminal hypothesis testing, 2) multiterminal parameter estimation, and 3) multiterminal pattern classification, in either case of positive rates or zero rates. In addition, the paper includes three new results, i.e., the converse theorems for all problems of multiterminal hypothesis testing, multiterminal parameter estimation, and multiterminal pattern classification at the zero rate.