On the existence of efficient estimators

The common signal processing problem of estimating some nonrandom parameter s of a signal in additive noise is considered. The problem investigated in this paper is under what conditions an efficient estimator exists, i.e., an unbiased estimator with a variance equal to the Cramer-Rao lower bound (CR B). It is well known that if the signal is linear or, more generally, affin e in the parameters and the noise Gaussian, an efficient estimator does exi st. This paper shows that under some conditions, this is the only case wher e an efficient estimator exists.