Tuning Parameter Selectors For The Smoothly Clipped Absolute Deviation Method

The penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables,but also produces estimators which are as efficient as the oracle estimator. However, these attractive features depend on appropriately choosing the tuning parameter. Wang et al. (2007) have proved that the GCV method cannot select the tuning parameter satisfacto-rily, with a non-ignorable over-fitting effect in the resulting model. So they proposed a new tuning parameter selector BIC(λ) which was able to identify the true model consis-tently. In this paper, we investigate other tuning parameter selectors, such as AIC(λ), AICu(λ), BICu(λ), RIC(λ) and so on. We show that BICu(λ) and RIC(λ) method are also consistence, and BICu(λ) is better than BIC(λ) method. In addition, we studied the situation of small-sample and showed that AICu(λ) was more effective when the sample were not large. At the end of the theory part, we also study the tuning parameter selection with a converging parameters, accordingly, we give two more consistent selectors. In the Simulation studies are presented to support theoretical findings.