Optimal Experimental Design for High-Dimensional Asymptotically Optimal Confidence Regions

• Activity Number: 134 - Design of Experiments: Case Studies and Advancements
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Binjie Luo* and Kent Eskridge
• Companies: University of Nebraska-Lincoln and University of Nebraska-Lincoln
• Keywords: Supersaturated design; high-dimensional inference; experimental design; high-dimensional experimental design; lasso

Abstract

This report defines an optimality criteria for supersaturated designs that is based on an underlying inference methodology, the asymptotically optimal confidence regions for high-dimensional data Van de Geer et al. [The Annals of Statistics, 42(3):1166-1202, 2014], which has been shown to have good theoretical properties, as well as expected coverage on simulated data. The criteria is defined for confidence intervals of single components from a supersaturated design. Supersaturated designs with a better criteria should produce shorter desparsified lasso confidence intervals while maintaining the expected coverage. An optimal condition for single component confidence intervals is also derived.