Tutorial: Methodologies for sufficient dimension reduction in regression

Title & Authors
Tutorial: Methodologies for sufficient dimension reduction in regression
Yoo, Jae Keun;

Abstract
In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $\small{k^{th}}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.
Keywords
Hessian matrix;inverse regression;least squares;permutation test;seeded dimension reduction;sufficient dimension reduction;
Language
English
Cited by
1.
Dimension reduction for right-censored survival regression: transformation approach, Communications for Statistical Applications and Methods, 2016, 23, 3, 259
2.
Intensive numerical studies of optimal sufficient dimension reduction with singularity, Communications for Statistical Applications and Methods, 2017, 24, 3, 303
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