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

摘要

In this paper we derive some new and practical results on testing andinterval estimation problems for the population eigenvalues of a Wishart matrixbased on the asymptotic theory for block-wise infinite dispersion of thepopulation eigenvalues. This new type of asymptotic theory has been developedby the present authors in Takemura and Sheena (2005) and Sheena and Takemura(2007a,b) and in these papers it was applied to point estimation problem ofpopulation covariance matrix in a decision theoretic framework. In this paperwe apply it to some testing and interval estimation problems. We show that theapproximation based on this type of asymptotics is generally much better thanthe traditional large-sample asymptotics for the problems.