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Forward Regression for Ultra-High Dimensional Variable Screening
Open accessAbstract
Motivated by the seminal theory of Sure Independence Screening (Fan and Lv 2008, SIS), we investigate here another popular and classical variable screening method, namely, forward regression (FR). Our theoretical analysis reveals that FR can identify all relevant predictors consistently, even if the predictor dimension is substantially larger than the sample size. In particular, if the dimension of the true model is finite, FR can discover all relevant predictors within a finite number of steps. To practically select the “best” candidate from the models generated by FR, the recently proposed BIC criterion of Chen and Chen (2008) can be used. The resulting model can then serve as an excellent starting point, from where many existing variable selection methods (e.g., SCAD and Adaptive LASSO) can be applied directly. FR’s outstanding finite sample performances are confirmed by extensive numerical studies.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
Cited by
Feature Screening via Distance Correlation Learning
Li, R., Zhong, W., & Zhu, L. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.695654 · Cited by 747
Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension
Wang, L., Wu, Y., & Li, R. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.656014 · Cited by 323
Tuning Parameter Selection in High Dimensional Penalized Likelihood
Fan, Y., & Tang, C. Y. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12001 · Cited by 256
Metadata
- Authors
- Wang, H.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2009-12
- Volume
- 104
- Issue
- 488
- Pages
- 1512-1524
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W3122008423
- Cited by
- 366
- References
- 3
- FWCI
- 10.66
- Type
- journal article
- Language
- en
- Open access
- green
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