Estimating functions of canonical correlation coefficients

Abstract

Let [rho]21,...,[rho]2p be the squares of the population canonical correlation coefficients from a normal distribution. This paper is concerned with the estimation of the parameters [delta]1,...,[delta]p, where [delta]i = [rho]2i/(1 - [rho]2i), i = 1,...,p, in a decision theoretic way. The approach taken is to estimate a parameter matrix [Delta] whose eigenvalues are [delta]1,...,[delta]p, given a random matrix F whose eigenvalues have the same distribution as r2i/(1 - r2i), i = 1,...,p, where r1,...,rp are the sample canonical correlation coefficients.