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Shrinkage tuning parameter selection with a diverging number of parameters (2008)
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BibTeX
@TECHREPORT{Wang08shrinkagetuning,
author = {Hansheng Wang and Bo Li and Chenlei Leng and Hansheng Wang and Bo Li and Chenlei Leng},
title = {Shrinkage tuning parameter selection with a diverging number of parameters},
institution = {},
year = {2008}
}
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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, Ma and Zhang, 2007). Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang, Li, and Tsai (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. Consequently, our theoretical results further enlarge not only the applicable scope of the traditional
