  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 (2005) and Sheena and Takemura
(2007a,b) and in these 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 is generally much better than
the traditional large-sample asymptotics for the problems.
