Some Notes on the Nonnegative Garrote

Abstract

Some notes on the use of the nonnegative garrote (NG) are given in this article. The main result is that, compared with other penalized least-squares methods, the NG has a natural selection of penalty function according to an estimator of prediction risk. Furthermore, two natural estimators of the tuning parameter which only involve very simple computations are proposed corresponding to the Akaike information criterion (AIC) and Bayesian information criterion (BIC), respectively. This indicates that to select tuning parameters, it may be unnecessary to optimize a model selection criterion repeatedly. Several reasonable NG estimators with natural tuning parameters are proposed for multicollinearity problems and other problems. Simulation results and a real data analysis are reported for testing the results obtained previously.