A Note on The Moments of Stochastic Shrinkage Parameters in Ridge Regression

Abstract

A common problem in econometric models and multiple regression in general is multicollinearity, which produces undesirable effects on the Least Squares estimators. A possible solution to this problem is the "Ridge" Regression estimator proposed by Hoerl and Kennard (1970). Ridge Regression has been applied to such diverse areas as economics, marketing and the calibration of instruments in industrial processes. However, the properties of these estimators crucially depend upon the selection of certain biasing parameters which are stochastic. In this regard several proposals have been made and the purpose of this paper is to derive general expressions for the moments of the stochastic biasing parameters. With this knowledge we expect to stablish conditions under which a Ridge Regression estimator is better than others.