Hoerl, Arthur E.; Kennard, Robert W. (2000, ASQ and American Statistical Association) University of Delaware; E. I. du Pont de Nemours & Co.
[This abstract is based on the authors' abstract.] In multiple regression, it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X'X. The ridge trace is introduced, this being a method for demonstrating the effects of nonorthogonality in two dimensions. It then is shown how to augment X'X to obtain biased estimates with smaller mean square error.
Augmentation,Orthogonal array (OA),Multiple regression,Estimation