Tuning parameter selectors for the smoothly clipped absolute deviation method

Wang, Hansheng; Li, Runze; Tsai, Chih‐Ling

doi:10.1093/biomet/asm053

Cited by 635 publications

(389 citation statements)

References 25 publications

(49 reference statements)

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“…This phenomenon has been observed by Broman & Speed (2002), Siegmund (2004), and Bogdan et al (2004) in genetic studies. Wang et al (2007) also noticed that BIC is liberal in general. Smalln-large-P situations are abundant, see Donoho (2000), Singh et al (2002), Marchini et al (2005), Clayton et al (2005), Fan and Li (2006), Zhang and Huang (2008), and Hoh et al (2008).…”

Section: Introductionmentioning

confidence: 98%

Extended BIC for small-n-large-P sparse GLM

Chen¹,

Chen²

2012

STAT SINICA

149

134

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SummaryThe small-n-large-P situation has become common in genetics research, medical studies, risk management, and other fields. Feature selection is crucial in these studies yet poses a serious challenge. The traditional criteria such as AIC, BIC, and crossvalidation choose too many features. To overcome the difficulties caused by the small-n-large-P situation, Chen and Chen (2008) developed a family of extended Bayes information criteria (EBIC). Under normal linear models, EBIC is found to be consistent with nice finite sample properties. Proving consistency for non-normal and nonlinear models poses serious technical difficulties. In this paper, through a number of novel techniques, we establish the consistency of EBIC under generalized linear models in the small-n-large-P situation. We also report simulation results and a real-data analysis to illustrate the effectiveness of EBIC for feature selection.

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Section: Introductionmentioning

confidence: 98%

Extended BIC for small-n-large-P sparse GLM

Chen¹,

Chen²

2012

STAT SINICA

149

134

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“…Apart from the papers already mentioned, there has been a recent surge of publications establishing the 'oracle' property for a variety of penalized maximum likelihood or related estimators (e.g., Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004, Li & Liang (2007), Wang & Leng (2007), Wang, G. Li and Jiang (2007), Wang, G. Li and Tsai (2007), Wang, R. Li and Tsai (2007), Yuan & Lin (2007), Zhang & Lu (2007), Zou & Yuan (2008), Zou & Li (2008), Johnson et al (2008)). The 'oracle' property also paints a misleading picture of the behavior of the estimators considered in these papers; see the discussion in Leeb & Pötscher (2005), Yang (2005), Pötscher (2007), Pötscher & Leeb (2007), Leeb & Pötscher (2008b).…”

Section: Introductionmentioning

confidence: 99%

On the distribution of the adaptive LASSO estimator

Pötscher

Schneider

2009

Journal of Statistical Planning and Inference

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We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The largesample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than n −1/2 in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the 'oracle' property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator. The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.MSC 2000 subject classification. Primary 62F11, 62F12, 62E15, 62J05, 62J07.

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“…Wang, Li, and Tsai (2007) show that the use of generalized cross validation to select λ does not necessarily achieve model-selection consistency.…”

Section: Choosing the Penalty Parametermentioning

confidence: 97%

Variable selection and estimation in high-dimensional models

Horowitz¹

2015

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Models with high-dimensional covariates arise frequently in economics and other fields. Often, only a few covariates have important effects on the dependent variable. When this happens, the model is said to be sparse. In applications, however, it is not known which covariates are important and which are not. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases. Methods are available for a wide variety of linear, nonlinear, semiparametric, and nonparametric models. The performance of some of these methods in finite samples is illustrated through Monte Carlo simulations and an empirical example.

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Tuning parameter selectors for the smoothly clipped absolute deviation method

Cited by 635 publications

References 25 publications

Extended BIC for small-n-large-P sparse GLM

Extended BIC for small-n-large-P sparse GLM

On the distribution of the adaptive LASSO estimator

Variable selection and estimation in high-dimensional models

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