Multiterminal Estimation Extensions and a Geometric Interpretation

In multiterminal estimation the basic theoretical question is to prove the existence of encod ing and decoding schemes that can achieve a certain rate of compression while resulting in a particular statistical estimation e ciency This is by comparison a much less studied eld than multiterminal source coding Essentially only two approaches have been reported Zhang and Berger established an upper bound on the asymptotic estimation e ciency under certain rate compatibility constraints and a test channel constraint referred to as the solvability condi tion Han and Amari tightened the upper bound under weaker constraints on both the rates and the test channel distributions However their bound is in most cases prohibitively complex to compute Here we unify the two approaches We are able to construct an upper bound that is asymptotically equal to Han and Amari s bound under the same rate compatibility condi tions Our bound is valid under weaker constraints on the test channels than those of Zhang and Berger Moreover the bound is easily computed for most source distributions We also present a new geometric interpretation of the upper bound on asymptotic estimation e ciency Introduction Assume that the sources Xn and Y n are i i d according to p x y where is a possibly vector valued parameter We assume the existence of an estimator
X Y n which is asymptotically unbiased We assume the estimator has an asymptotic co variance index V where