The Distribution of Stochastic Shrinkage Parameters in Ridge Regression

Abstract

In this article we derive the density and distribution functions of the stochastic shrinkage parameters of three well-known operational Ridge Regression estimators by assuming normality. The stochastic behavior of these parameters is likely to affect the properties of the resulting Ridge Regression estimator, therefore such knowledge can useful in the selection of the shrinkage rule. Some numerical calculations are carried out to illustrate the behavior of these distributions, throwing light on the performance of the different Ridge Regression estimators.