On Uniform Asymptotically Efficient Estimation of a Constant Signal in Additive Noise of Unknown Structure

The article considers the problem of extracting an unknown constant signal that is observed in additive symmetrical noise with unknown probability distribution density. Asymptotically efficient estimates (in both the weak and the strong sense) of this signal are constructed, that are uniform with respect to certain natural sets of densities. The basic condition that is imposed on these sets is that they be compact in the corresponding normed spaces.