|
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.
|
