This paper presents a solution of a nonlinear prediction problem for processes {X_t, t ∈ IR} having regular versions of conditional distributions for X_t given the past, which are symmetric and unimodal, relative to an increasing symmetric (not necessarily convex) loss function vanishing at the origin. These processes include the Gaussian family. The result depends on a variational inequality due to S. Sherman and a simple self-contained proof of the latter is included.
展开▼
