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Activity Number: 152 - Recent Development in Sufficient Dimension Reduction
Type: Topic Contributed
Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
Sponsor: International Statistical Institute
Abstract #323280 View Presentation
Title: Simultaneous Variable Selection and Structural Dimension Estimation in Sufficient Dimension Reduction
Author(s): Haileab Hilafu* and Wenbo Wu
Companies: University of Tennessee and University of Oregon
Keywords: Sufficient Dimension Reduction ; MAVE ; Group Lasso
Abstract:

In sufficient dimension reduction, there are three main goals: determine the structural dimension of the central subspace, estimate the basis directions of the central subspace, and select active predictors by obtaining sparse basis directions. These are often achieved independently in sequence of stages. In this study, we develop a method that achieves all three simultaneously under the minimum average variance estimation framework. We impose a double shrinkage that helps us to estimate the central subspace, its structural dimension, and perform variable selection in one pass. Our method is shown to be consistent and more stable than existing methods in which the estimation accuracy of each of these is affected by the accuracy in estimating the others. A detailed algorithm is provided to implement the proposed method, and a comprehensive simulation study is carried out to examine its effectiveness and compare it to other existing methods.


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