Asymptotic distribution of the increase of the largest canonical correlation when one of the vectors is augmented |
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| Authors: | Robert A. Wijsman |
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| Affiliation: | University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 USA |
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| Abstract: | Let r1 > r2 > … be the sample canonical correlations in a sample of size n from a multivariate normal population partitioned into two subvectors with population canonical correlations 1 > 2 > …. Let one of the subvectors be augmented by adding one or more variables to it. For the increase in the largest canonical correlation, Δr in the sample and Δ in the population, it is shown that √n(Δr − Δ) → DN(0, σ2) and a formula for σ2 is derived. |
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| Keywords: | increase of largest canonical correlation augmented vector asymtotic distribution |
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