Comparison of Two Factor Subspaces

Chen and Robinson's (J. Multivariate Anal.8 190-203 (1989)) recent method of comparison of factors spaces of two related populations is formalized and extended to the case of sums of eigenspaces of two compact self-adjoint operators. The factor subspaces are defined as finite sets of each operator's eigenspace and then compared by canonical analysis using sample approximations. A test of existence of a sub-space common to the two factor subspaces is then developed, without normality assumptions, but only with conditions on moments.