Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 4, 717--733

Inference on Eigenvalues of Wishart Distribution Using Asymptotics with respect to the Dispersion of Population Eigenvalues

Yo Sheena, Shinshu University, Japan
Akimichi Takemura, University of Tokyo, Japan

SUMMARY. 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.

AMS (2000) subject classification. Primary 62F12; secondary 62F03, 62F25.

Key words and phrases. Eigenvalues of covariance matrix, Wishart distribu- tion, test on eigenvalues, interval estimation of eigenvalues.

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