| Abstract: | A method called FICYREG of estimating regression coefficients is introduced. This is a generalization to the multivariate regression problem of the James-Stein estimator. When suitably représentés FICYREG emerges as a rule in which the canonical variates and canonical correlations have an intrinsic role to play. By exploiting these objects FICYREG is able to achieve stability against the influence of the “noise” present in problems where the responses are correlated so that some of the response vector's canonical variates will be essentially independent of all others including the predictors. The least squares (LS) estimator is, by contrast, highly sensitive to this noise. The use of FICYREG is illustrated in terms of an example, and its peformance is compared to the LS estimator when a quadratic loss function is assumed. The cases of both fixed and random predictors are considered. Overall, FICYREG outperforms the LS estimator. |
