THE EFFICIENCY OF THE ASYMPTOTIC EXPANSION OF THE DISTRIBUTION OF THE CANONICAL VECTOR UNDER NONNORMALITY

In canonical correlation analysis, canonical vectors are used in the interpretation of the canonical variables. We are interested in the asymptotic representation of the expectation, the variance and the distribution of the canonical vector. In this study, we derive the asymptotic distribution of the canonical vector under nonnormality. To obtain the asymptotic expansion of the canonical vector, we use a perturbation method. In addition, as an example, we show the asymptotic distribution with an elliptical population. Key words and phrases: Asymptotic distribution, canonical correlation analysis, canonical vector, elliptical population, perturbation method, small sample. 1