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...

In this paper we study an asymptotic version of the holonomic efficiency problem originated in the study of swimming microorganism. Given a horizontal distribution on a vector bundle, the holonomy of a loop in the base space is the displacement along the fiber direction of the end points of its horizontal lift. The holonomic efficiency problem is to find the most efficient loop in the base spac...