ON OPTIMAL ESTIMATION WITH RESPECT TO A LARGE FAMILY OF COST-FUNCTIONS

被引：3

作者：

HALL, EB ^{[1
]}

WISE, GL ^{[1
]}

机构：

[1] UNIV TEXAS,DEPT ELECT & COMP ENGN,AUSTIN,TX 78712

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1991年 / 37卷 / 03期

关键词：

OPTIMAL NONLINEAR ESTIMATION; NON-MEAN-SQUARE-ERROR FIDELITY CRITERIA; REGRESSION FUNCTIONS;

D O I：

10.1109/18.79934

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Consider two random variables X and Y. A commonly encountered problem involves estimating X via h(Y) so as to minimize E[PHI(X - h(Y))] where h is Borel measurable and PHI is a Borel measurable cost function chosen to adequately reflect the fidelity demands of the problem under consideration. This correspondence places a mild condition on the regular conditional distribution of X given sigma(Y) that ensures that E[PHI(X - h(Y))] is minimized for any cost function PHI that is nonnegative, even, and convex. In addition, it is shown that given any Borel measurable function g: R --> R, there exist random variables X and Y possessing a joint density function such that E[X\Y = y] = g(y) a.e., with respect to Lebesgue measure.

引用

页码：691 / 693

页数：3