Tuning parameter selectors for the smoothly clipped absolute deviation method

Hansheng Wang, Runze Li, Chih Ling Tsai

Research output: Contribution to journalArticle

418 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)553-568
Number of pages16
JournalBiometrika
Volume94
Issue number3
DOIs
StatePublished - Sep 14 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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