Hotelling's T2 tests in paired and independent survey samples: An efficiency comparison

Hotelling's T2 tests in paired and independent survey samples are compared using the traditional asymptotic efficiency concepts of Hodges-Lehmann, Bahadur and Pitman, as well as through criteria based on the volumes of corresponding confidence regions. Conditions characterizing the superiority of a procedure are given in terms of population canonical correlation type coefficients. Statistical tests for checking these conditions are developed. Test statistics based on the eigenvalues of a symmetrized sample cross-covariance matrix are suggested, as well as test statistics based on sample canonical correlation type coefficients.