Distributional Expansions for Canonical Correlations from Contingency Tables
M. E. O’Neill · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1978
Summary The asymptotic distribution of the canonical correlations from contingency tables was investigated by the author (1978) for a general theoretical correlation structure. In this paper, the structure examined is one in which all theoretical, non-zero correlations are different. For the observed canonical correlations corresponding to non-zeros, an analytic expansion is obtained enabling not only the asymptotic distributions to be obtained, but also a correction for “bias”. A condition is found for determining when the sum of the canonical components corresponding to zero correlations is distributed as χ2.