Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
Transformed sufficient dimension reduction
Language
English
Abstract
© 2014 Biometrika Trust. We propose a general framework for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. Themain idea is to first transformeach of the raw predictors monotonically and then search for a low-dimensional projection in the space defined by the transformed variables. Both user-specified and data-driven transformations are suggested. In each case, the methodology is first discussed in generality and then a representative method is proposed and evaluated by simulation. The proposed methods are applied to a real dataset.
Keywords
Minimum average variance estimation, Monotone smoothing spline, Predictor transformation, Probability integral transformation, Sliced inverse regression
Publication Date
2014
Source Publication Title
Biometrika
Volume
101
Issue
4
Start Page
815
End Page
829
Publisher
Oxford University Press
DOI
10.1093/biomet/asu037
Link to Publisher's Edition
http://dx.doi.org/10.1093/biomet/asu037
ISSN (print)
00063444
ISSN (electronic)
14643510
Recommended Citation
Wang, T., X. Guo, L. Zhu, and P. Xu. "Transformed sufficient dimension reduction." Biometrika 101.4 (2014): 815-829.