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Biometrika Advance Access first published online on August 5, 2007
This version published online on August 8, 2007
Biometrika, doi:10.1093/biomet/asm053
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Copyright © 2007 Biometrika Trust

Article

Tuning parameter selectors for the smoothly clipped absolute deviation method

Hansheng Wang

Guanghua School of Management, Peking University, Beijing, China, 100871

Runze Li

Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, Pennsylvania 16802-2111, U.S.A.

Chih-Ling Tsai

Graduate School of Management, University of California, Davis, California 95616-8609, U.S.A.

hansheng{at}gsm.pku.edu.cn

rli{at}stat.psu.edu

cltsai{at}ucdavis.edu

Received for publication 1 November 2005. Revision received 1 November 2006.
  Abstract

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 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.

Key Words: AIC • BIC • Generalized crossvalidation • Least absolute shrinkage and selection operator • Smoothly clipped absolute deviation


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