Forward Regression for Ultra-High Dimensional Variable Screening

By Hansheng Wang. 2009

397 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8bb843b4f274d77c60944e5ac7365a2f36d76c7d

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Citations in the corpus

Covariance Regression Analysis (2017, neutral): “A similar condition can be found in Bickel and Levina (2008a, 2008b) and Wang (2009).”
Linear regression (2012, neutral): “Accordingly, the Cp criterion is defined as an estimate of E ‖ μ − ŷ ‖2 /σ 2, Cp = SSE σ̂ 2 + 2(k + 1) − n, (28)”
Model-Free Feature Screening for Ultrahigh Dimensional Data (2011, methodology): “A large number of well-known variable screening and selection approaches, such as linear SIS (Fan and Lv 2008), Lasso (Tibshirani 1996), stepwise regression, and forward regression (Wang 2009) have been proposed in the literature.”
Tuning parameter selection in high dimensional penalized likelihood (2013, methodology): “For each simulated data set, we calculate the penalized MLE β̂ λ using (2.3) with ℓn(β) being the log-likelihood function for the linear regression model (5.1).”
High dimensional ordinary least squares projection for screening variables (2015, methodology): “e <1, we can choose a submodel with size n, n 1 or n=logn(Fan and Lv, 2008; Li, Peng, et al., 2012), or using techniques such as extended BIC (Chen and Chen, 2008) to determine the submodel size (Wang, 2009). For simplicity, we mainly use n 11 as the submodel size in numerical study, with some ex”
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models (2009, background): “Recently, Wang (2009) showed that under certain technical conditions, forward selection also can achieve the sure screening property.”
Statistical significance in high-dimensional linear models (2012, methodology): “…(SIS) method (Fan and Lv, 2008), and high-dimensional variable screening or selection properties have been established for forward variable selection (Wang, 2009) and for the PC-algorithm (B¨uhlmann, Kalisch and Maathuis, 2010) (“PC” stands for the ﬁrst names of its in-ventors, Peter Spirtes and…”
Feature Screening via Distance Correlation Learning (2012, methodology): “The normality assumption has been widely used in the area of ultrahigh-dimensional data analysis to facilitate the technical derivations; see, for example, Fan and Lv (2008) and Wang (2009).”
Quantile Correlations and Quantile Autoregressive Modeling (2012, neutral): “…literature , for example, Machado and Silva (2005) for count data, Mu and He (2007) for power transformed data, Peng and Huang (2008) and Wang and Wang (2009) for survival analysis, He and Liang (2000) and Wei and Carroll (2009) for regression with measurement error, Ando and Tsay (2011) for…”
Targeted Undersmoothing. (2017, methodology): “2Alternatives to the lasso estimator with similar properties include the Dantzig selector (see [19]), forward stepwise regression (see [54], [57], [48], [28], [37] ), SCAD (see [30]), and many others.”
A variational Bayes approach to variable selection (2017, background): “[69] showed that this criterion performs well in several contexts.”