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Activity Number: 38 - Advances in Variable Selection
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #306415 Presentation
Title: Simultaneous Confidence Regions for Coefficients in High-Dimensional Linear Models
Author(s): Xiaorui Zhu* and Peng Wang and Yichen Qin
Companies: University of Cincinnati and University of Cincinnati and University of Cincinnati
Keywords: Penalized likelihood; variable/feature selection; solution paths; confidence set; bootstrap

Constructing simultaneous confidence regions for model selection is of great value and will provide practically useful insights of what variables we should confidently select, and what variables are nearly irrelevant or even significantly irrelevant. Based on the very stable selection method by partitioning the solution paths (SPSP), we propose a method to construct simultaneous confidence regions (named: confidence tube(ConfTube)) over the selection of residual bootstraps. The simultaneous confidence regions can help one to answer the three questions above simultaneously. We build the theoretical properties for it and show its advantage among several popular methods by a few numerical studies. Likewise, a real data example is used to illustrate the methodology proposed in this article.

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

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