Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods

By Zhishen Ye, Robert E. Weiss. 2003

236 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4c952e3682bbdc0f9af62d649a99176a0b6e9e4b

How researchers see this paper

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

In Computational Mechanics

1. R. Dennis Cook
2. Bing Li
3. Xiangrong Yin
4. Yanyuan Ma
5. Liping Zhu
6. Hansheng Wang
7. Yingcun Xia
8. Jiawei Yao

In Mathematical Physics

1. Lingzhou Xue
2. R. Dennis Cook
3. Hansheng Wang
4. Liliana Forzani
5. Peng Zeng
6. Wei Luo
7. Yu Zhu
8. Jiawei Yao

In Numerical Analysis

1. Lingzhou Xue
2. R. Dennis Cook
3. Hansheng Wang
4. Liliana Forzani
5. Peng Zeng
6. Wei Luo
7. Yu Zhu
8. Jiawei Yao

Citations in the corpus

• On estimation efficiency of the central mean subspace (2014, methodology): “…test procedure in Cook and Li (2004), the crossvalidation procedure in Xia et al. (2002) and Xia (2007), the Bayesian information criterion BIC type of criterion in Zhu et al. (2006) and the bootstrap procedure in Ye and Weiss (2003), Li and Dong (2009), Dong and Li (2010), Ma and Zhu (2012), etc.”
• Likelihood-Based Sufficient Dimension Reduction (2009, methodology): “Many dimension reduction methods have been proposed since the original work on SIR and SAVE.”
• Sufficient Dimension Reduction via Inverse Regression (2005, methodology): “Recently, Ye and Weiss (2003) proposed bootstrap methods to combine information from SIR and SAVE.”
• Sliced Regression for Dimension Reduction (2008, methodology): “Both Ye and Weiss (2003) and Zhu and Zeng (2006) demonstrated that if the true structure dimension were indeed d0 = 1 then the estimation variability associated with the second spurious direction should be large, which in turn would make the overall estimation variability with d = 2 large.”
• Combining eigenvalues and variation of eigenvectors for order determination (2016, methodology): “In this sense, Theorem 2 covers the consistency of the minimizer of the bootstrap criterion in Ye & Weiss (2003) as a special case.”
• Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, background): “Bootstrap test (Ye and Weiss, 2003) should also work well in this context.”
• Sufficient Dimension Reduction via Distance Covariance (2016, methodology): “Bootstrap method to estimate d has been used by Ye and Weiss (2003) and Zhu and Zeng (2006).”
• Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression (2006, methodology): “Next, we follow the basic idea of Ye and Weiss (2003) to develop the bootstrap procedure for choosing q in FC (or FM).”
• Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors (2016, methodology): “…subspace, including the sequential tests (Li 1991, Li and Wang 2007), the permutation test (Cook and Weisberg 1991), the bootstrap procedure (Ye and Weiss, 2003), the cross-validation method (Xia et al., 2002; Wang and Xia, 2008), the BIC type procedure (Zhu, Miao and Peng 2006), and the…”
• On Directional Regression for Dimension Reduction (2007, methodology): “The first group includes SIR, PHD, SAVE, SIRII (Li 1991), SCR, and GCR; the second group includes the convex combinations of (SIR, SAVE), (SIR, PHD), and (SIR, SIRII), with the coefficients determined by bootstrap, as proposed by Ye and Weiss (2003).”
• Asymptotics for sliced average variance estimation (2007, background): “ASYMPTOTICS FOR SAVE 3 It is worth pointing out that the study of SAVE should receive more attention, as several papers have revealed that SAVE is more comprehensive than SIR: under regularity conditions, the CDR space of SAVE actually contains that of SIR (see [6, 24]).”