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Accession Number:
ADA063983
Title:
The Relation between Statistical Decision Theory and Approximation Theory.
Corporate Author:
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Report Date:
1978-10-01
Abstract:
The approximation theory model describes a class of optimality principles in statistical decision theory as follows. Let S be the risk set of a statistical decision problem, that is, S R sub phi theta, theta an element of Theta, phi an element of Phi where Phi is the collection of randomized decision procedures, Theta is the parameter space and R sub phitheta is the risk function of the statistical decision procedure phi. We interpret S as a set in the normed linear space L. Let vvtheta satisfy vtheta or R sub phi for all phi an element of Phi and all theta an element of Theta. Then s sub 0 an element of S is said to be v,L optimal if abs. val. s sub 0-v or abs. val. s-v for all s an element of S. It is easily seen that many well-known optimality principles of statistics are of this type, such as Bayes rules and minimax rules. In this paper, characterization theorems for this class of optimality principles are given.
Descriptive Note:
Technical summary rept.,
Supplementary Note:
Prepared in cooperation with Munich Univ. (West Germany). Mathematisches Inst. der Technischen.
Pages:
0014
Contract Number:
DAAG29-75-C-0024
File Size:
6.32MB
