A criterion for selecting information- preserving data reductions for use in the design of multiple-parameter estimators

A scalar measure of the fractional amount of the total information for parameter estimation that is retained when a record of raw data is reduced to a given statistic is introduced. This measure, the relative information index (RII), is a function of Fisher's information matrices for the statistic and for the raw data, and it resembles an efficiency measure in that it acquires values between zero and one. A criterion, based on the RII, is formulated for statistic selection, and some applications are discussed.