High-dimensional asymptotic expansions for the distributions of canonical correlations

Yasunori Fujikoshi and Tetsuro Sakurai

Journal of Multivariate Analysis, 2009, vol. 100, issue 1, 231-242

Abstract: This paper examines asymptotic distributions of the canonical correlations between and with q [infinity] and c=p/n-->c0[set membership, variant][0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher's z-transformation is proposed. Then, the asymptotic distributions are improved further by deriving their asymptotic expansions. Numerical simulations revealed that our approximations are more accurate than the classical approximations for a large range of p,q, and n and the population canonical correlations.

Keywords: primary; 62H10 secondary; 62E20 Asymptotic distributions Canonical correlations Extended Fisher's z-transformation High-dimensional framework (search for similar items in EconPapers)
Date: 2009
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