Estimating the structural dimension of regressions via parametric inverse regression

By Efstathia Bura, R. Dennis Cook. 2001

151 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aeb77eef1a190a55d25e65938521b17d90dc65cb

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In Control and Systems Engineering

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Citations in the corpus

Dimension reduction for conditional mean in regression (2002, methodology): “parametric inverse regression (PIR, Bura and Cook 2001 ).”
Asymptotics for pooled marginal slicing estimator based on SIRα approach (2005, background): “Moreover, Bura [4] and Bura and Cook [5] proposed a parametric version of SIR-I.”
Testing predictor contributions in sufficient dimension reduction (2004, methodology): “The asymptotic distribution of T ′n(d) can be found by using results of Bura and Cook (2001a).”
Dimension reduction for the conditional mean in regressions with categorical predictors (2003, methodology): “…ordinary least squares [OLS; Li and Duan (1989)], sliced inverse regression [SIR; Li (1991)], sliced average variance estimation [SAVE; Cook and Weisberg (1991)], principal Hessian directions [PHD; Li (1992); see also Cook (1998b)] and parametric inverse regression [PIR; Bura and Cook (2001)].”
Dimension reduction for nonelliptically distributed predictors (2009, methodology): “These include Ordinary Least Squares (OLS) [Li and Duan (1989)], Sliced Inverse Regression (SIR) [Li (1992)], Parametric Inverse Regression (PIR) [Bura and Cook (2001)], Canonical Correlation [Fung et al. (2002)] and Kernel Inverse Regression (KIR) [Zhu and Fang (1996), Ferre and Yao (2005)].”
Moment-based dimension reduction for multivariate response regression (2006, background): “Their work, which to some degree is parallel to Li, Cook and Chiaromonte (2003), can be thought of as an extension of univariate OLS under missing link (Li and Duan, 1989) to multivariate OLS.”
Dimension reduction for the conditional kth moment in regression (2002, methodology): “Although modifications of SIR have been proposed (see, for example, Schott (1994) and Velilla (1998)) they all share the estimation of SE(ZIy) as a common goal.”
Smoothed Functional Inverse Regression (2005, methodology): “Moreover, other methods have been proposed for estimating ED: pHd (Li (1992)), SAVE (Cook (1991)), PIR (Bura and Cook (2001)), MAVE (Xia, Tong, Li and Zhu (2002)), estimation of the Central Mean Subspace (Cook and Li (2002)) and use of the conditional kth moment (Yin and Cook (2002)).”
On Sliced Inverse Regression With High-Dimensional Covariates (2006, methodology): “Bura and Cook (2001a) suggested a general weighted chi-squared sequential test that does not require the assumption that covariates follow a normal distribution.”
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).”