Dimension reduction for conditional mean in regression

By R. Dennis Cook, Bing Li. 2002

427 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/83761d64815e2c2351eaeb0e1537b2f7b0b8b7c6

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Partial martingale difference correlation (2015, background): “In particular, Shao and Zhang [10] proposed the notion of martingale difference divergence (MDD, hereafter) and martingale difference correlation (MDC, hereafter) to measure the conditional mean (in)dependence of Y given X (Y is said to be conditionally mean independent of X provided that E(Y”
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.”
Asymptotics for sliced average variance estimation (2007, methodology): “, βk), there are several proposed methods for estimating the projection directions B/space that is spanned by B, such as projection pursuit regression (PPR) [11], the alternating conditional expectation (ACE) method [1], principal Hessian directions (pHd) [17], minimum average variance estimation (M”
A Multiple-Index Model and Dimension Reduction (2008, background): “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).”
Minimax risks for sparse regressions: Ultra-high-dimensional phenomenons (2010, neutral): “Dimension reduction methods are often studied in more general settings than linear regression [17, 26].”
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.”
Kernel dimension reduction in regression (2009, background): “In this case, pHd fails to find the true subspace; this is due to the fact that pHd is incapable of estimating a direction that only appears in the variance [8].”
Sliced Regression for Dimension Reduction (2008, methodology): “Similarly, if the intersection of all MDR subspaces is still a MDR subspace, then it is called the CMS (Cook and Li 2002).”
A Model-Free Test for Reduced Rank in Multivariate Regression (2003, methodology): “Our generalized rank test is based on the central mean subspace (CMS) recently introduced by Cook and Li (2002) for univariate regressions (r D 1).”
Nonlinear sufficient dimension reduction for functional data (2017, background): “That is, we seek a few linear combinations of X that are sufficient to describe the conditional distribution of Y given X [see Cook and Weisberg (1991), Li (1991), Cook (1998), Cook and Li (2002)].”
Model checking for parametric single‐index models: a dimension reduction model‐adaptive approach (2016, background): “Y |X/, is called the structural dimension (Cook and Li, 2002).”
Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “The central mean subspace ( Cook and Li, 2002 ) is a subspace of the CS designed to characterize just the mean function E(Y |X).”