This paper discusses the problem of estimating a functional from noisy observations of other functionals in the same class. For the case of convex functional classes and linear functionals, the solution to the problem is well known [1]. Magaril-Il’yaev et al. solved several generalizations of the problem.

Here, Darkhovsky uses his previous work to solve the recovery problem of a more general class of nonlinear functionals. An optimal solution is found under rather general random errors. Three examples are given to estimate a function, its first derivative, and its integral, by a set of given noisy observations. The paper will interest numerical analysts and engineers.