Some results on canonical correlation and their applications to a linear model Original Research Article

We show the monotonic properties of canonical correlation coefficients and the concave–convex properties of some of their functions with respect to some elements of the variance–covariance corresponding to them, and then use these results to discuss the monotonic and concave–convex properties of the relative efficiency of the least squares estimator (LSE) in a linear regression model with respect to some elements of the variance–covariance of the error vector. Finally we give two examples of the two-stage sampling regression model and pairwise overlapping sampling regression model.