On a Class of Estimates of the Location Parameters

A class of estimates of a signal in additive noise with zero mean that have the form $\overline{X}-\overline{\Phi(X_i-\overline{X})}$, is studied. An asymptotic formula is obtained for the mean-square error of such estimates, and it is shown that an asymptotically optimal (in the minimax sense) estimate can always be obtained in such a form by appropriate choice of the function $\Phi$ if the noise distribution density $p(x)$ is not exactly known, and only finitely many integrals of the form $\int\varphi_j(x)p(x)dx$ are known.