Abstract
Let ρ 1,…, ρ p be the population canonical correlation coefficients from a normal distribution. This paper considers the estimation of δ 1,…, δ p , where δ i=ρ i 2/(1−ρ i 2), i=1,…,p , in a decision theoretic way. Since the distribution of δ i 's is complicated, two-staged estimation has been a usual method so far; i.e., first find a good estimator of a matrix whose eigenvalues are the δ i 's, then use its eigenvalues as the estimators of δ i 's. In this paper we directly estimate δ i 's and evaluate the estimators with respect to a quadratic loss function. We propose a new class of estimators and prove its dominance over the usual estimator.
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