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- W4381799559 abstract "Let (X, Z) be a bivariate random vector. A predictor of X based on Z is just a Borel function g(Z). The problem of least squares prediction of X given the observation Z is to find the global minimum point of the functional E[(X − g(Z))2] with respect to all random variables g(Z), where g is a Borel function. It is well known that the solution of this problem is the conditional expectation E(X|Z). We also know that, if for a nonnegative smooth function F: R×R → R, arg ming(Z)E[F(X, g(Z))] = E[X|Z], for all X and Z, then F(x, y) is a Bregmann loss function. It is also of interest, for a fixed ϕ to find F (x, y), satisfying, arg ming(Z)E[F(X, g(Z))] = ϕ(E[X|Z]), for all X and Z. In more general setting, a stronger problem is to find F (x, y) satisfying arg miny∈RE[F (X, y)] = ϕ(E[X]), ∀X. We study this problem and develop a partial differential equation (PDE) approach to solution of these problems." @default.
- W4381799559 created "2023-06-24" @default.
- W4381799559 creator A5089096605 @default.
- W4381799559 date "2023-06-23" @default.
- W4381799559 modified "2023-09-26" @default.
- W4381799559 title "A PDE Approach to the Problems of Optimality of Expectations" @default.
- W4381799559 doi "https://doi.org/10.28924/2291-8639-21-2023-57" @default.
- W4381799559 hasPublicationYear "2023" @default.
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