Determining the Dimensionality in Sliced Inverse Regression

By James R. Schott. 1994

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

1. Chenlei Leng
2. Bing Li
3. Kenji Fukumizu
4. Jianqing Fan
5. Hansheng Wang
6. Lixing Zhu
7. R. Dennis Cook
8. Heng Peng

Citations in the corpus

• Sufficient Forecasting Using Factor Models (2015, methodology): “Several methods such as Li (1991) and Schott (1994) have been proposed to determine L .”
• Sufficient Dimension Reduction via Inverse Regression (2005, methodology): “Schott (1994) investigated inference methods for dimension when the predictors follow an elliptically contoured distribution.”
• The sliced inverse regression algorithm as a maximum likelihood procedure (2009, background): “Among them, we can cite Li (1991), Schott (1994) and Ferré (1998).”
• Asymptotics for pooled marginal slicing estimator based on SIRα approach (2005, methodology): “Note that determining the numberK (of indices) is considered by Li [16], Schott [20] and Ferré [9], for the SIR-I method.”
• A note On outlier sensitivity of Sliced Inverse Regression (2002, background): “SIR has been investigated in several articles with emphasis on its asymptotic properties (Li, 1991; Hsing and Carroll, 1992; Kötter, 1996; Zhu and Fang, 1996) and on the estimation of the dimension K of the edr space in a pre-step of SIR (Li, 1991; Schott, 1994; Ferré, 1997; 1998).”
• Extending Sliced Inverse Regression (2001, background): “Schott (1994) proposed a test that requires elliptically symmetric regressors and for which the tuning constant is the number of observations c per slice, as opposed to the number of slices H of Li (1991).”
• Combining eigenvalues and variation of eigenvectors for order determination (2016, background): “• Sequential test In the sufficient dimension reduction contexts, sequential tests are developed by Li (1991), Schott (1994), Cook & Li (2004), and Bura & Yang (2011), among others.”
• Optimal sufficient dimension reduction in regressions with categorical predictors (2002, background): “Extensions of this distributional result were studied by Cook [(1998), Chapter 11], Schott (1994) and Velilla (1998).”
• Testing predictor contributions in sufficient dimension reduction (2004, methodology): “in this article uses fixed slicing in which the number of observations per slice grows with the sample size. Zhu 26 R. D. COOK and Fang (1996) bypass the slicing step and use kernel smoothing instead. Schott (1994)investigated inference methodsfor d whenthe predictorsfollow an elliptically contoured ”
• Estimating the structural dimension of regressions via parametric inverse regression (2001, background): “In contrast, SIR and its variants (Schott, 1994; Velilla, 1998) require the subjective a priori choice of a tuning constant, such as the number of slices, which is not suggested by the observed data but is rather arbitrarily selected.”
• DECIDING THE DIMENSION OF EFFECTIVE DIMENSION REDUCTION SPACE FOR FUNCTIONAL AND HIGH-DIMENSIONAL DATA (2010, methodology): “Existing methods for deciding the dimensionality of EDR space in the multivariate setting [Li (1991), Schott (1994)] are not directly applicable to the types of data that are focused on in this paper.”
• DIMENSION REDUCTION BASED ON CANONICAL CORRELATION (2002, methodology): “Schott (1994) considered using both the first and second moments of the conditional distribution of x given y, and developed a chi-square test valid for any elliptically symmetric predictor distribution.”
• Applied Multivariate Statistical Analysis (2003, background): “It is possible to combine SIR and SIR II (Cook and Weisberg, 1991; Li, 1991; Schott, 1994) directly, or to investigate higher conditional 18.4 Boston Housing 439 moments.”
• Moment-based dimension reduction for multivariate response regression (2006, methodology): “On the other hand, the efficacy of the methodology based on nonparametric estimation of the inverse curves, encompassing SIR, SAVE and their variations (e.g. Schott, 1994, Velilla 1998), may be hindered by the curse of dimensionality.”
• A New Dimension Reduction Approach for Data-Rich Marketing Environments: Sliced Inverse Regression (2000, background): “More generally, if independent variables are elliptically distributed, Schott (1994) provides an appropriate procedure to determine the number of factors to retain.”
• Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “…one can in principle determine the dimension d by carrying out a sequential asymptotic test based on the asymptotic distribution of the estimator of SY |Z, along the lines of Li (1991, 1992), Schott (1994), and Cook and Li (2004), the full asymptotic development is beyond the scope of this paper.”
• Gradient-Based Kernel Dimension Reduction for Regression (2014, methodology): “While many methods have been developed for the choice of dimensionality 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…”