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Ridge Regression: Biased Estimation for Nonorthogonal Problems
Arthur E. Hoerl and Robert W. Kennard
Vol. 42, No. 1, Special 40th Anniversary Issue (Feb., 2000), pp. 80-86
Published by: Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality
Stable URL: http://www.jstor.org/stable/1271436
Page Count: 7
You can always find the topics here!Topics: Eigenvalues, Estimation bias, Statistical estimation, Least squares, Estimators for the mean, Mathematical vectors, Point estimators, Mathematical theorems, Statistical variance, Mathematical functions
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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.
Technometrics © 2000 American Statistical Association