Title: Optimal design for penalized estimators
Authors: Jonathan Stallrich - North Carolina State University (United States) [presenting]
Maria Weese - Miami University (United States)
Kade Young - North Carolina State University (United States)
Byran Smucker - Miami University (United States)
David Edwards - Virginia Commonwealth University (United States)
Abstract: The experimental design community has gravitated towards penalized estimation (e.g., Dantzig selector and lasso) to analyze data from screening experiments that may assume factor sparsity. However, the optimal design framework is largely based on statistical properties of unpenalized least-squares estimation. The purpose is to review the current theory relating design properties to the support recovery properties of the lasso and Dantzig selector. An optimal design framework is then proposed that better tailors design selection to maximizing the probability of support recovery. A local optimality approach is considered first and demonstrates that the optimal design assuming all positive model coefficients is not orthogonal. We then use the proposed framework to justify popular heuristic measures for constructing supersaturated designs in which the number of runs is less than the number of factors. A more robust optimal design framework is then considered that assumes less knowledge of the true model. To optimize the computationally-expensive criteria, we propose a construction algorithm that starts with many efficient designs according to the heuristic measures.