Minimax Ridge Regression Estimation.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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The technique of ridge regression has become a popular tool for data analysts faced with a high degree of multicollinearity in their data. By using a ridge estimator, it was hoped that one could both stabilize the estimates lower the condition number of the design matrix and improve upon the squared error loss of the least squares estimator. Recently classes of ridge regression estimators have been developed which dominate the usual estimator in risk, and hence are minimax. This paper derives conditions that are necessary and sufficient for minimaxity of a large class of ridge regression estimators. The conditions derived here are very similar to those derived for minimaxity of some Stein-type estimators.
- Statistics and Probability