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

TL;DR

This paper develops new asymptotic methods for testing and estimating population eigenvalues of Wishart matrices, showing improved accuracy over traditional large-sample approaches.

Contribution

It applies a novel asymptotic theory for block-wise infinite dispersion of eigenvalues to testing and interval estimation, enhancing accuracy.

Findings

Asymptotic approximations outperform traditional methods in accuracy.

New methods are practical for eigenvalue testing and estimation.

The approach is based on recent developments in asymptotic theory.

Abstract

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.