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Regularization Parameter Selections via Generalized Information Criterion
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DOI：10.1198/jasa.2009.tm08013.png)
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摘要
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We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators This approach relies heavily on the choice of regularization parameter, which controls the model complexity In this paper, we propose employing the generalized in criterion. encompassing the commonly used Akaike in criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter Our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches We show that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001) In contrast, however, the AIC-type selector tends to overfit with positive probability We further show that the AIC-type selector is asymptotically loss efficient. while the BIC-type selector is not Our simulation results confirm these theoretical findings. and an empirical example is presented Some technical proofs are given in the online supplementary material
Keyword:
Akaike information criterion
Bayesian information criterion
Least absolute shrinkage and selection operator
Nonconcave penalized likelihood
Smoothly clipped absolute deviation
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