Robust Estimates of a Function

The class of estimates of function values that was introduced in [A. B. Tsybakov, Probl. Peredachi Inf., 1982, vol. 18, no. 2, pp. 44–60] is considered. The asymptotic distribution and convergence of the moments of the estimates is established. A solution is offered for the problem of choosing a robust estimation strategy, i.e., of choosing estimates from the class under consideration that are optimal in the sense of the minimax of the asymptotic standard error.