COMPARISON OF SOME BIASED ESTIMATION METHODS (INCLUDING ORDINARY SUBSET REGRESSION) IN THE LINEAR MODEL

摘要

We discuss ridge, Marquardt's generalized inverse, shrunken, and principal components estimators. The discussion is with respect to the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. We find that, as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector;that biased estimators all introduce constraints on the parameter space;that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity;and that ordinary least-squares subset regression is the best overall method.