Shrinkage Estimation for High Dimensional

• Activity Number: 148
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Xiaoli Gao and Ejaz Syed Ahmed*+
• Companies: Oakland university and Brock University
• Keywords: Asymptotic risk ; Lasso ; Ridge regression ; shrinkage estimation ; Sparse model ; High dimensional data

Abstract

In high-dimensional data settings where p > n, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable selection methods, including Lasso and its generations, cannot distinguish covariates with weak and no contribution. Thus, prediction based on a subset model of selected covariates may not be efficient. We propose a high-dimensional shrinkage estimation strategy to improve the prediction performance of a subset model. A high-dimensional shrinkage estimator is constructed by shrinking a weighted ridge estimator in the direction of a pre-defined candidate subset. Under an asymptotic distributional quadratic risk criterion, its prediction performance is explored analytically. We show that proposed high-dimensional shrinkage estimator performs better than the weighted ridge estimator. It improves the prediction performance of any candidate subset model generated from most existing Lasso-type variable selection methods. The relative performance of the proposed shrinkage strategy is demonstrated by both simulation studies and the real data analysis.