A PDE Approach to the Problems of Optimality of Expectations
| dc.contributor.author | Hasanov, Mahir | |
| dc.date.accessioned | 2024-03-13T10:33:11Z | |
| dc.date.available | 2024-03-13T10:33:11Z | |
| dc.date.issued | 2023 | |
| dc.department | İstanbul Beykent Üniversitesi | en_US |
| dc.description.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 : RxR & RARR; 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 & phi; to find F (x, y ), satisfying, arg ming(Z)E[F (X, g(Z))] = & phi;(E[X|Z]), for all X and Z. In more general setting, a stronger problem is to find F (x, y) satisfying arg miny & ISIN;RE[F (X, y)] = & phi;(E[X]), & FORALL;X. We study this problem and develop a partial differential equation (PDE) approach to solution of these problems. | en_US |
| dc.identifier.doi | 10.28924/2291-8639-21-2023-57 | |
| dc.identifier.issn | 2291-8639 | |
| dc.identifier.scopusquality | Q4 | en_US |
| dc.identifier.uri | https://doi.org/10.28924/2291-8639-21-2023-57 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12662/3823 | |
| dc.identifier.volume | 21 | en_US |
| dc.identifier.wos | WOS:001021285600002 | en_US |
| dc.identifier.wosquality | N/A | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Etamaths Publ | en_US |
| dc.relation.ispartof | International Journal Of Analysis And Applications | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | expectation | en_US |
| dc.subject | conditional expectation | en_US |
| dc.subject | random variables | en_US |
| dc.subject | Bregman loss functions | en_US |
| dc.subject | partial differential equations | en_US |
| dc.title | A PDE Approach to the Problems of Optimality of Expectations | en_US |
| dc.type | Article | en_US |
