Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression

By Yu Zhu, Peng Zeng. 2006

148 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/01260ea8a93d19635c766845841b0dc6489681b8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. Kenji Fukumizu
2. Francis R. Bach
3. Michael I. Jordan
4. Bing Li
5. Arthur Gretton
6. Xiangrong Yin
7. Yingcun Xia
8. Hansheng Wang

In Computer Vision and Pattern Recognition

1. Kenji Fukumizu
2. Luc Van Gool
3. Michael I. Jordan
4. Dacheng Tao
5. Francis R. Bach
6. Trevor Darrell
7. Ming-Hsuan Yang
8. Li Fei-Fei

In Statistics and Probability

1. Yingcun Xia
2. Xiangrong Yin
3. Bing Li
4. Kenji Fukumizu
5. Wenhui Sheng
6. Hansheng Wang
7. Francis R. Bach
8. R. Dennis Cook

Citations in the corpus

• On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, unknown): “(1991, 1992), Cook and Weisberg (1991), Xia, Tong, Li, and Zhu (2002), Cook and Li (2002, 2004), Yin and Cook (2002), Bura and Cook (2001), Fung, He, Liu, and Shi (2002), Li, Zha, and Chiaromonte (2005), Cook and Ni (2005), and Zhu and Zeng (2006).”
• Sequential sufficient dimension reduction for large p, small n problems (2015, methodology): “This model is an example of Zhu and Zeng (2006).”
• Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “Zhu and Zeng (2006) proposed a method that targets the central mean subspace of the characteristic function of the conditional density of Y |X.”
• Sufficient Dimension Reduction via Distance Covariance (2016, methodology): “Zhu and Zeng (2006) and Zeng and Zhu (2010) proposed the Fourier transform method and integral transform method, respectively.”
• Sufficient dimension reduction based on an ensemble of minimum average variance estimators (2011, methodology): “It is used by Zhu and Zeng (2006) to recover the central mean subspace and central subspace, respectively, based on the assumption that X is multivariate normal.”
• Sliced Regression for Dimension Reduction (2008, methodology): “For the Fourier method, σ 2T = 1.0, but σ 2W = 5% or 10% (Zhu and Zeng 2006).”
• Kernel dimension reduction in regression (2009, methodology): “s the central subspace based on an expected log likelihood [35]. This requires, however, an estimate of the joint probability density, and is limited to single-index regression. Finally, Zhu and Zeng [36] have proposed a method for estimating the central subspace based on the Fourier transform. This”
• The sliced inverse regression algorithm as a maximum likelihood procedure (2009, unknown): “…1991), principal Hessian directions (Li, 1992; Cook, 1998), inverse regression (Cook and Ni, 2005), graphical methods (Cook, 1994; Cook and Wetzel, 1993), simple contour regression (Li et al., 2005), Fourier estimation (Zhu and Zeng, 2006) and principal fitted components (PFC) (Cook, 2007).”
• Shrinkage inverse regression estimation for model‐free variable selection (2009, methodology): “The data consist of 195 instances with complete records, and Zhu and Zeng (2006) concluded it reasonable to infer that the dimension of the central subspace equals 2.”