广义相关系数和若干极值

GENERALIZED CORRELATION COEFICIENTS AND SOME EXTREMES

对于矩阵D_1和D_2是非负定时,本文给出行列式之比|X'AY|~2/(|X'D_1X||Y'D_2Y|和矩阵之迹[tr(X’AY)]~2在约束X’D_1X=I_k,Y’D_2Y=I_k的极值,这一结果把作者文[5]的极值结果推广到D_1,D_2可能奇异的情况。本文把所得到的极值结果应用到多元分析,说明文章[1]定义的几种广义相关系数的极值性质,从而分别给出几种广义相关系数一种统计解释。

In this paper, we give extremes of the ratio of determinantsand the trace of matrix [tr(X'AY]2 under contrains X' D1X = IK and Y' D2Y = IK when D1 and D2 are non-negative definite. Results obtained are the generalizations of the results obtained by author[5] when DI and D2 are positive definite. These extremes are applied to multivariate analysis. The extreme properties of generlized Correlation Coefficients between two random vecters definitted by paper[1] are obtained, so that statistical meanings of generalized correlation coefficients are also explained.