D-Optimal Designs Based on the Second-Order Least Squares Estimator

• Activity Number: 165
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Lucy Gao* and Julie Zhou
• Companies: and University of Victoria
• Keywords: optimal design ; asymmetric distribution ; convex optimization ; moment theory ; polynomial regression ; trigonometric regression

Abstract

When the error distribution in a regression model is asymmetric, the second-order least squares estimator (SLSE) is more efficient than the ordinary least squares estimator. This result motivated the research in Gao and Zhou (2014), where A-optimal and D-optimal design criteria based on the SLSE were proposed and various design properties were studied. In this paper, we continue to investigate the optimal designs based on the SLSE and develop new theories for the D-optimal designs. Using convex optimization techniques and moment theories, we can construct D-optimal designs for polynomial and trigonometric regression models with any continuous design space. Several theoretical results are derived. The methodology is quite general and can be applied to reduced polynomial models, reduced trigonometric models, and other regression models.