Shrinkage Tuning Parameter Selection with a Diverging Number of Parameters

Journal of Royal Statistical Society, Series B, Forthcoming

25 Pages Posted: 2 Dec 2008

See all articles by Hansheng Wang

Hansheng Wang

Peking University - Guanghua School of Management

Bo Li

Tsinghua University - School of Economics & Management

Chenlei Leng

University of Warwick

Date Written: September 28, 2008

Abstract

Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g., LASSO, SCAD, etc) are found particularly useful for the purpose of variable selection (Fan and Peng, 2004; Huang et al., 2007b). Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang et al. (2007b) and Wang and Leng (2007) demonstrated that the tuning parameters selected by a BIC-type criterion can identify the true model consistently. In this work, similar results are further extended to the situation with a diverging number of parameters for both unpenalized and penalized estimators (Fan and Peng, 2004; Huang et al., 2007b). Consequently, our theoretical results further enlarge not only the applicable scope of the traditional BIC-type criteria but also that of those shrinkage estimation methods (Tibshirani, 1996; Huang et al., 2007b; Fan and Li, 2001; Fan and Peng, 2004).

Keywords: BIC, Diverging Number of Parameters, LASSO, SCAD

JEL Classification: C5, C51

Suggested Citation

Wang, Hansheng and Li, Bo and Leng, Chenlei, Shrinkage Tuning Parameter Selection with a Diverging Number of Parameters (September 28, 2008). Journal of Royal Statistical Society, Series B, Forthcoming . Available at SSRN: https://ssrn.com/abstract=1308335

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Bo Li

Tsinghua University - School of Economics & Management ( email )

Beijing, 100084
China

Chenlei Leng

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

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