Finite Sample Properties of A-Optimal Designs for Binary Response Data

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Srichand Jasti* and Rajesh Nandy and Karabi Nandy
• Companies: University of North Texas Health Science Center and University of North Texas Health Science Center and UCLA
• Keywords: Optimal Design ; Cramer-Rao ; numerical methods

Abstract

A-optimality refers to the design that minimizes the sum of variances of the estimators of all parameters in a model. By virtue of Cramer-Rao bound, the trace of the Information matrix for the parameters serve as a lower bound for the sum of variances of the estimators and the bound is attained asymptotically. Hence, asymptotically, A-optimality is achieved by minimizing the trace of the Information matrix. For a binary response experiment with a logit model the asymptotic solution is known to be a two point design which is point symmetric but not weight symmetric. For non-linear models, Cramer-Rao bound is crude for finite samples and hence the asymptotic solution can be very different from the design that minimizes the sum of variances. Here we will explore the validity of the asymptotic solution by directly minimizing the sum of variances using numerical methods in a restricted search space. It will be demonstrated that even in a very restrictive search space of point symmetric designs, the theoretical solution is half as efficient for a sample size of 100. Further improvement can be achieved by relaxing the restriction of the solution being point symmetric.