Asymptotic Expansions for the Distributions of Characteristic Roots When the Parameter Matrix Has Several Multiple Roots11This research was supported by National Science Foundation grant GP-11473.

Abstract

This chapter focuses on the asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix in case of several multiple population roots. Li and Pillai have studied the problem of finding the asymptotic expansion of the roots of S1S2-1 in case of one extreme multiple population roots. The chapter presents an extension of their results to the case when there are several multiple population roots. The chapter also focuses on the asymptotic expansion for MANOVA in case of several multiple population roots, and on asymptotic expansion for canonical correlation in case of several multiple population roots.