Estimation of the Mean in a Normal Set

The estimation of a signal in Gaussian white noise is discussed. It is well known that the arithmetic mean estimator $\overline x$ can be improved if certain a priori information is known about the possible values of the signal parameter. Corrections to $\overline x$ are formulated [see Eqs. (6) and (8)] such that the risk for a quadratic loss function coincides with the minimum risk up to higher-order terms than the risk of $\overline x$ under various assumptions concerning the a priori signal density function.