Variable Selection Diagnostics Measures for High-Dimensional Regression

• Activity Number: 579
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: JCGS-Journal of Computational and Graphical Statistics
• Author(s): Yuhong Yang*+ and Ying Nan
• Companies: University of Minnesota and University of Minnesota
• Keywords: model selection ; variable selection deviation ; model selection diagnostics ; high-dimensional regression

Abstract

Many exciting results have been obtained on model selection for high-dimensional data in both efficient algorithms and theoretical developments. The powerful penalized regression methods can give sparse representations of the data even when the number of predictors is much larger than the sample size. One important question then is: How do we know when a sparse pattern identified by such a method is reliable? In this work, we propose variable selection deviation (VSD) measures that give one a proper sense on how many predictors in the selected set are likely trustworthy. Indeed, under some conditions, the VSD measures weakly consistently estimate the number of true terms missing and also the number of wrong term used in a selected model. Simulation and a real data example demonstrate the utility of these measures for application.

Model selection diagnostics are severely missing both in research and application. Suitable model selection diagnostics measures can much improve quality of decisions based on statistical data analysis.