%0 Journal Article %1 hoerl1970ridgeregression %A Hoerl, Arthur E. %A Kennard, Robert W. %D 1970 %I American Statistical Association and American Society for Quality %J Technometrics %K ill-posed_problems inverse_problems regularization ridge_regression statistics %N 1 %P pp. 55-67 %T Ridge Regression: Biased Estimation for Nonorthogonal Problems %U http://www.jstor.org/stable/1267351 %V 12 %X 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. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.

@article{hoerl1970ridgeregression, 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. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.}, added-at = {2012-03-27T17:26:32.000+0200}, author = {Hoerl, Arthur E. and Kennard, Robert W.}, biburl = {https://www.bibsonomy.org/bibtex/210f24c0e95cde40632d497415f804576/peter.ralph}, copyright = {Copyright © 1970 American Statistical Association and American Society for Quality}, description = {The original citation for "ridge regression".}, interhash = {6468748d5b4b1f5d02107b4c131e9ea6}, intrahash = {10f24c0e95cde40632d497415f804576}, issn = {00401706}, journal = {Technometrics}, jstor_articletype = {research-article}, jstor_formatteddate = {Feb., 1970}, keywords = {ill-posed_problems inverse_problems regularization ridge_regression statistics}, language = {English}, number = 1, pages = {pp. 55-67}, publisher = {American Statistical Association and American Society for Quality}, timestamp = {2012-03-27T17:26:32.000+0200}, title = {Ridge Regression: Biased Estimation for Nonorthogonal Problems}, url = {http://www.jstor.org/stable/1267351}, volume = 12, year = 1970 }