Confidence Regions and Intervals for Sparse Penalized Regression with Random Designs

• Activity Number: 388
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Liang Yin*+ and Shu Lu and Yufeng Liu
• Companies: University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill
• Keywords: confidence interval ; penalized regression ; random design ; non-convex ; optimization ; variational inequality

Abstract

During the past decade, sparse regularized regression has been prevalent in high dimensional data analysis due to the advantage of simultaneous variable selection and prediction. A number of convex as well as non-convex penalties have been proposed in the literature to achieve sparsity. Despite intense work in this area, it is still a challenge to perform valid inference for sparse regularized regression with a general penalty. In this talk, by making use of state-of-the-art optimization tools in stochastic variational inequality theory, we propose a unified method to construct confidence intervals for estimated coefficients using a wide range of penalties, including the well-known non-convex SCAD and MCP penalties. We study the inference for the population version of a regularized regression under mild assumptions, which gives a clear underlying model for consideration. Some theoretical properties of the proposed method are obtained. Numerical simulations and real data examples are presented to demonstrate the validity and effectiveness of the proposed inference procedure.