Sufficient Dimension Reduction via Inverse Regression

By R. Dennis Cook, Liqiang Ni. 2005

359 citations recorded by the source corpus.

Subfields: Computational Mechanics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6f9eba404e997c2dc1bcb1d75075a2090852e0a3

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

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Likelihood-Based Sufficient Dimension Reduction (2009, background): “Cook and Ni (2005) proposed inverse regression estimation (IRE) for estimating SSIR which is asymptotically efficient among methods based on first conditional moments.”
Dimension reduction for nonelliptically distributed predictors (2009, background): “The similar problem arises frequently in dimension reduction; for example, it arises also in Xia et al. (2002), Cook and Ni (2005) and Cook (2007).”
Precision Medicine. (2019, methodology): “One could also use methods for feature construction in regression to identify the set of candidate features ℬ (Cook and Ni 2005; Li 2007; Lee and Verleysen 2007).”
Fused Estimators of the Central Subspace in Sufficient Dimension Reduction (2014, methodology): “As stated in Theorem 1 from Cook and Ni (2005), √ n(vec(ζ̂ (j ) ) − vec(ζ (j ))), j = 1, 2, converges in distribution to a normal with mean 0 and nonsingular covariance matrix j .”
Marginal tests with sliced average variance estimation (2007, methodology): “For sliced average variance estimation, Cook & Ni (2005) suggested a test for dimension derived using a method similar to that used by Li for sliced inverse regression.”
Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “CS estimation methods like IRE (Cook and Ni, 2005) and its ancestor SIR (Li, 1991) require that E(X|γTX = ν) be a linear function of ν. Partitioning the range of a continuous response into intervals Hs, s = 1, . . . , h, this linearity condition implies that ξs ≡ Var(X) −1{E(X|Y ∈ Hs) − E(X)} ∈ SY…”
Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression (2006, background): “|X] or SY|X. Recently, Cook and Ni (2005) proposed the minimum discrepancy method, which is more efficient than spectral decomposition for estimating SE[Y”
Sufficient Dimension Reduction via Squared-Loss Mutual Information Estimation (2010, background): “LSMI inherits good properties from MLMI and, moreover, provides an analytic SMI estimator that gives an analytic formula for its derivative (see Table 1).”
Shrinkage inverse regression estimation for model‐free variable selection (2009, methodology): “Predictor conditional independence hypothesis tests have been developed for SIR, the CIRE and other members of the IRE family (Cook, 2004; Cook and Ni, 2005, 2006).”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, neutral): “(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).”
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).”
Asymptotics for sliced average variance estimation (2007, background): “Note that Cook and Ni ([8], Section 7) investigated the asymptotic behavior of the slicing estimator of the SAVE matrix and reported a result that is relevant to Theorem 2.”