期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2007
卷号：69
期号：04
出版社：Indian Statistical Institute
摘要：In this paper, we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population eigenvalues. This new type of asymptotic theory has been developed by the present authors in Takemura and Sheena ({\it JMA}, 2005) and Sheena and Takemura ({\it Stat. Methodol.}, 2007; {\it JMA}, 2008), and in those papers, it was applied to point estimation problem of population covariance matrix in a decision theoretic framework. In this paper, we apply it to some testing and interval estimation problems. We show that the approximation based on this type of asymptotics can be widely used as a good alternative to the traditional approximation based on large-sample asymptotics.
关键词：Eigenvalues of covariance matrix, Wishart distribu- tion, test on eigenvalues, interval estimation of eigenvalues.
