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Ridge Regression: Biased Estimation for Nonorthogonal Problems

Arthur E. Hoerl and Robert W. Kennard
Technometrics
Vol. 42, No. 1, Special 40th Anniversary Issue (Feb., 2000), pp. 80-86
DOI: 10.2307/1271436
Stable URL: http://www.jstor.org/stable/1271436
Page Count: 7
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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.

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