Minimax Linear Smoothing for Capacities

Minimax linear smoothers are considered for the problem of estimating a homogeneous signal field in an additive orthogonal noise field. A minimax game with the quadratic-mean estimation error as an objective function is used to formulate this problem. Uncertainty in signal and noise field spectra is modeled using general nonparametric classes of measures proposed by Huber and Strassen for the problem of minimax hypothesis testing. These classes, which are described in terms of Choquet alternating capacities of order 2, include the conventional models for spectral uncertainty and admit a general solution to the minimax linear smoothing problem.