On Directional Regression for Dimension Reduction

By Bing Li, Shaoli Wang. 2007

520 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Genetics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d1bd95110eb7e53615d863de856bf9874ed3d4cf

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Citations in the corpus

Combining eigenvalues and variation of eigenvectors for order determination (2016, methodology): “The method used to obtain the matrix M̂ is Directional Regression (Li & Wang, 2007).”
Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors (2016, methodology): “Because the true factors ft has identity covariance matrix, the form of the kernel matrix adopted in the theorem coincides with its original form in Li and Wang (2007). However, it does make a modification on the latter when the estimated factors f̂t are used instead, which no longer have identity c”
Nonlinear sufficient dimension reduction for functional data (2017, methodology): “For example, other dimension reduction methods in the classical setting, such as Directional Regression [Li and Wang (2007)], can be generalized in to functional nonlinear SDR in a similar manner.”
A Semiparametric Approach to Interpretable Machine Learning (2020, methodology): “Examples include sliced inverse regression [23], sliced average variance estimation [7], and directional regression [22].”
A general theory for nonlinear sufficient dimension reduction: Formulation and estimation (2013, methodology): “…heteroschedastic conditional variance operator can be used to generate nonlinear extensions of other second-order SRD methods such as contour regression [Li, Zha and Chiaromonte (2005)], directional regression [Li and Wang (2007)], SIR-II [Li (1991)] and other F2M methods [Cook and Forzani (2009)].”
Likelihood-Based Sufficient Dimension Reduction (2009, methodology): “With a ¼ 1, model 4 is identical to simulation model I used by Li and Wang (2007).”
Dimension reduction for nonelliptically distributed predictors (2009, methodology): “Second-moment-based methods such as Sliced Average Variance Estimator [Cook and Weisberg (1991)], Principal Hessian Directions [Li (1992)] and Directional Regression [Li and Wang (2007)] require, in addition, the constant conditional variance assumption.”
Sufficient Dimension Reduction via Distance Covariance (2016, background): “For instance, sliced average variance estimation (SAVE; Cook and Weisberg 1991), inverse regression (IR; Cook and Ni 2005), and directional regression (DR; Li and Wang 2007).”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, background): “2005), and directional regression (Li and Wang 2007).”
Gradient-Based Kernel Dimension Reduction for Regression (2014, methodology): “…in respective dimension reduction methods (Schott, 1994, Ferr´e, 1998, Cook and Lee, 1999, Bura and Cook, 2001, Yin and Seymour, 2005, Li and Wang, 2007, Li et al., 2011, to list some), they are derived from asymptotic analysis of some test statistics, which may not be practical in…”
ldr: An R Software Package for Likelihood-Based Su?cient Dimension Reduction (2014, methodology): “Among these methods are the sliced average variance estimation (SAVE, Cook and Weisberg 1991), principal Hessian directions (PHD, Li 1992), directional regression (Li and Wang 2007), and the inverse regression estimation (IRE, Cook and Ni 2005).”