Dimension reduction for the conditional kth moment in regression

By Xiangrong Yin, R. Dennis Cook. 2002

175 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b234f712120e9b940ac8a61280b39d73d149d139

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

On Sliced Inverse Regression With High-Dimensional Covariates (2006, background): “If condition (3) is not satisfied, then, following the suggestion of Li (1991) and Cook and Weisberg (1991), we can explore higher conditional moments of x given y or consider the socalled “central kth-moment subspace” (CKMS) (Yin and Cook 2002).”
Sufficient dimension reduction based on an ensemble of minimum average variance estimators (2011, background): “In particular, it unifies the central mean subspace [Cook and Li (2002)], the central moment subspace [Yin and Cook (2002)], Fourier transform estimators [Zhu and Zeng (2006)], dMAVE [Xia (2007)] and sliced regression [Wang and Xia (2008)] in a coherent system.”
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 a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, unknown): “See Yin and Cook (2002).”
A Multiple-Index Model and Dimension Reduction (2008, methodology): “This article only considered the specification of dimension reduction in the conditional mean function (Samarov 1993; Hristache et al. 2001; Cook and Li 2002; Xia et al. 2002; Yin and Cook 2002; among others).”
Moment-based dimension reduction for multivariate response regression (2006, methodology): “The next proposition generalizes Proposition 1 of Yin and Cook (2002) and Cook and Setodji (2003).”
A constructive approach to the estimation of dimension reduction directions (2007, methodology): “und in the literature. In the last decade or so, a series of papers (e.g. H¨ardle and Stocker, 1989; Li, 1991; Cook and Weisberg, 1991; Samarov, 1993; Hristache, Juditski, Polzehl and Spokoiny, 2001; Yin and Cook, 2002; Xia, Tong, Li and Zhu, 2002; Cook and Li, 2002; Li, Zha and Chiaromonte, 2004; L”
Estimation for a partial-linear single-index model (2009, methodology): “…Hall (1989), Härdle, Hall and Ichimura (1993)]; the average derivative approach [Stoker (1986), Doksum and Samarov (1995) and Hristache, Juditsky and Spokoiny (2001)]; and sliced inverse regression (SIR) and related methods [Li (1991), Cook and Li (2002), Xia et al. (2002) and Yin and Cook (2002)].”
Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods (2003, methodology): “Formal tests (Li 1991, 1992; Cook 1998a,b; Cook and Lee 1999; Bura and Cook 2001; Yin and Cook 2002) are welcome supplements to our bootstrap.”
Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression (2006, methodology): “When defining the central kth-moment subspace, Yin and Cook (2002) considered the power transformations of Y , which are Yl with 1 ≤ l ≤ k.”
Sliced Regression for Dimension Reduction (2008, methodology): “By Proposition 2, Sy|x can be estimated consistently and exhaustively through the CMS of (2), which can be estimated efficiently by many existing methods, including MAVE (Xia et al. 2002) and the methods of Yin and Cook (2002).”