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MINIMAX TESTS FOR CONVEX CONES

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LUTZ DÜMBGEN

*Institut für Angewandte Mathematik, Universität
Heidelberg,*

Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany
(Received November 12, 1993; revised May 30, 1994)

**Abstract.**
Let (*P*_{theta}: *theta* \in **R**^{p}) be a simple shift
family of distributions on **R**^{p}, and let **K** \subset **R**^{p} be a
convex cone. Within the class of nonrandomized tests of **K** versus
**R**^{p} \ **K**, whose acceptance region *A* satisfies *A* = *A* + **K**, a
test with minimal bias is constructed. This minimax test is compared
to a likelihood ratio type test, which is optimal with respect to a
different criterion. The minimax test is mimicked in the context of
linear regression and one-sided tests for covariance matrices.

*Key words and phrases*:
Bias, convex cone, covariance
matrix, duality, linear regression, minimax test, union-intersection
principle.

**Source**
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