Better Subset Regression Using the Nonnegative Garrote

A new method, called the nonnegative (nn) garrote, is proposed for doing subset regression. It both shrinks and zeroes coefficients. In tests on real and simulated data, it produces lower prediction error than ordinary subset selection. It is also compared to ridge regression. If the regression equations generated by a procedure do not change drastically with small changes in the data, the procedure is called stable. Subset selection is unstable, ridge is very stable, and the nn-garrote is intermediate. Simulation results illustrate the effects of instability on prediction error.