Explicit and Constrained Generalized Ridge Estimation

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Abstract
A method, based upon minimizing estimators of the criteria E(L 1 2) and E(L 2 2), is given for selecting the k 1, in generalized ridge regression; an explicit, closed form solution is developed for the resulting estimator β* of the vector of parameters,β, in the linear regression model. A method is also proposed for obtaining constrained generalized ridge estimators, with constraints placed upon β*, to utilize a priori information concerning the signs of the model parameters along with ridge estimation. These and other ridge estimation procedures are then examined and compared with least squares or constrained least squares estimators in a Monte Carlo study which demonstrates their effectiveness. An example is given to indicate their behavior and use on an applied problem.

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