Testing predictor contributions in sufficient dimension reduction
By R. Dennis Cook. 2004
164 citations recorded by the source corpus.
We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean function and smoothing is not required. The general approach is based on sufficient dimension reduction, the idea being to replace the predictor vector with a lower-dimensional version without loss of information on the regression. Methodology using sliced inverse regression is developed in detail.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3d623c9ca6998f3cd1e6b73309b9688fb17865e3
How researchers see this paper
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In Statistics and Probability
- Robert Tibshirani
- Howard D. Bondell
- Trevor J. Hastie
- Lexin Li
- R. Dennis Cook
- Hansheng Wang
- Chih-Ling Tsai
- Yingcun Xia
Citations in the corpus
- A note on shrinkage sliced inverse regression (2005, methodology): “It follows from Cook (2004) that a basis for the span of the eigenvectors corresponding to the d largest eigenvalues of M C SIR can be obtained by minimising F(A, C)=Wh y=1 d f @ 1/2 y Z C y −AC y d2 over AµRp×d and C y µRd, with C=(C 1 , . . . , C h ).”
- Shrinkage inverse regression estimation for model‐free variable selection (2009, methodology): “The first is test based, including, for example, the approximate sliced inverse regression (SIR) based t-test (Chen and Li, 1998), the marginal co-ordinate test (Cook, 2004) and the gridded χ2-test (Li et al., 2005).”
- Prediction by Supervised Principal Components (2006, methodology): “These include the sliced inversed regression approach of Duan and Li (1991) and Li (1992) and the sufficient dimension reduction approaches used by Chiaromonte, Cook, and Li (2002) and Cook (2004).”
- Marginal tests with sliced average variance estimation (2007, methodology): “This type of procedure is also possible with sliced average variance estimation if we use a marginal coordinate hypothesis (Cook, 2004) that requires Syjx c V, where V is a specified subspace of IRP.”