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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

ISSN (print)

00063444

ISSN (electronic)

14643510

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