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Activity Number: 608
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #319107 View Presentation
Title: Testing-Based Variable Selection for High-Dimensional Linear Models
Author(s): Siliang Gong* and Kai Zhang and Yufeng Liu
Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
Keywords: variable selection ; cross validation ; p-value ; hypothesis testing ; high-dimensionality

Variable selection is fundamental in high-dimensional problems. Various variable selection methods have been developed recently, for example, forward stepwise regression, least angle regression, and many more. These methods have a sequential nature in selection as variables are added into the model one-by-one. For such procedures, it is crucial to find a stopping criterion. One of the most commonly used technique in practice is cross-validation (CV). However, CV has huge computational cost and is lack of statistical interpretation. To overcome these drawbacks, we introduce a flexible and efficient testing-based variable selection approach that could be incorporated with any sequential selection procedures. At each step of the selection, we test the overall signal in the remaining inactive variables using the maximal absolute partial correlation among the inactive variables with the response conditionally on active variables. Furthermore, we develop a stopping criterion using the stepwise $p$-value. Numerical studies show that the proposed method delivers very competitive performance in terms of both variable selection accuracy and computational complexity compared to CV.

Authors who are presenting talks have a * after their name.

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