Tuning parameter selectors for the smoothly clipped absolute deviation method

The penalized least squares approach with smoothly clipped absolutedeviation penalty has been consistently demonstrated to be anattractive regression shrinkage and selection method. It notonly automatically and consistently selects the important variables,but also produces estimators which are as efficient as the oracleestimator. However, these attractive features depend on appropriatechoice of the tuning parameter. We show that the commonly usedgeneralized crossvalidation cannot select the tuning parametersatisfactorily, with a nonignorable overfitting effect in theresulting model. In addition, we propose a BIC tuning parameterselector, which is shown to be able to identify the true modelconsistently. Simulation studies are presented to support theoreticalfindings, and an empirical example is given to illustrate itsuse in the Female Labor Supply data.