Ridge Regression: Biased Estimation for Nonorthogonal Problems Export

@article{Hoel Kennard70 , 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.}, author = {Hoerl, Arthur E. and Kennard, Robert W.}, citeulike-article-id = {5831046}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/1267351}, citeulike-linkout-1 = {http://www.jstor.org/stable/1267351}, doi = {10.2307/1267351}, issn = {00401706}, journal = {Technometrics}, keywords = {ridge}, number = {1}, pages = {55--67}, posted-at = {2009-10-19 17:18:49}, priority = {2}, publisher = {American Statistical Association and American Society for Quality}, title = {Ridge Regression: Biased Estimation for Nonorthogonal Problems}, url = {http://dx.doi.org/10.2307/1267351}, volume = {12}, year = {1970} }

TY - JOUR ID - Hoel Kennard70 L3 - citeulike-article-id:5831046 N2 - 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. IS - 1 JF - Technometrics SN - 00401706 EP - 67 TI - Ridge Regression: Biased Estimation for Nonorthogonal Problems PB - American Statistical Association and American Society for Quality VL - 12 SP - 55 KW - ridge AU - Hoerl, Arthur AU - Kennard, Robert PY - 1970/// UR - http://dx.doi.org/10.2307/1267351 ER -