THE MINIMAX DIRECTION FOR THE DIRECT PRODUCT OF A CONVEX CONE WITH ITSAPPLICATION TO TESTING PROBLEMS
Citation：
Shi ningzhong（史宁中）.THE MINIMAX DIRECTION FOR THE DIRECT PRODUCT OF A CONVEX CONE WITH ITSAPPLICATION TO TESTING PROBLEMS[J].Chinese Annals of Mathematics B,1992,13(1):80~85
Page view： 991Net amount： 667
Authors：
Shi ningzhong（史宁中）;
Abstract：
Let C be a closed convex cone in $R^k$ and let $C^k$ be the p-th direct product of C. This paper gives some results of tlie minimax direction with respect to $C^p$ and an inner product based on $\gamma \bigotimes \lambda$, where $\gamma$ is a $k\times k$ diagonal matrix with positive diagonal elements,$\lambda$ is a $p\times p$ positive definite matrix and $\gamma \bigotimes \lambda$ is the Kronecker product of $\gamma$ and $\lambda$. It is also shown that the results may be applied to test the homogeneity of k normal mean vectors where the mean vectors are restricted by a given partial order.
