Subset Regression with Stepwise Directed Search

SUMMARY Stepwise Directed Search is a combination of forward selection and a modification of backward elimination. Mallows' statistic C p is used as a criterion function in comparing subsets of different sizes. The method can select automatically the subset with the smallest C p . Alternatively a number of alternative good candidate subsets of any size can be obtained by using the results of the sweep operator efficiently. This limits the computational effort of subset selection to about three times more than required for estimation without subset selection. Subsets can be selected from any number of regressors, as long as the full set of regression variables can be swept without numerical difficulties. The performance of Stepwise Directed Search on practical data was excellent: it always found the minimum C p subset and in every example but one it found the best subsets of all sizes.