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Tuning parameter selectors for the smoothly clipped absolute deviation method. (English) Zbl 1135.62058
Summary: 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 the appropriate choice of the tuning parameter.
We show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily, with a nonignorable overfitting effect in the resulting model. In addition, we propose a BIC tuning parameter selector, which is shown to be able to identify the true model consistently. Simulation studies are presented to support theoretical findings, and an empirical example is given to illustrate its use in the Female Labor Supply data.

MSC:
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)
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