A note on automatic variable selection using smooth-threshold estimating equations

This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley--James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A <sc>bic</sc>-type criterion for tuning parameter selection is also proposed. It is shown that the criterion achieves consistent model selection. A numerical study confirms the performance of the method. Copyright 2009, Oxford University Press.