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Tutorial: Dimension reduction in regression with a notion of sufficiency
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 Title & Authors
Tutorial: Dimension reduction in regression with a notion of sufficiency
Yoo, Jae Keun;
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 Abstract
In the paper, we discuss dimension reduction of predictors in a regression of with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central -moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of and the conditional distribution of . A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.
 Keywords
central subspace;central -moment subspace;central mean subspace;dimension reduction subspace;regression;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  crossref(new windwow)
2.
Intensive numerical studies of optimal sufficient dimension reduction with singularity, Communications for Statistical Applications and Methods, 2017, 24, 3, 303  crossref(new windwow)
3.
Tutorial: Methodologies for sufficient dimension reduction in regression, Communications for Statistical Applications and Methods, 2016, 23, 2, 105  crossref(new windwow)
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