Construction of A-optimal Designs for Linear Models

Abstract

For estimating parameters of a statistical model, it is important to minimize the variances of the estimators. Efficiency of an estimator increases as its variance becomes smaller. Sometimes instead of minimizing the variances of the individual parameters, it is important to minimize the total or average variance of all the parameter estimators. This refers to A-optimality in the context of optimal experimental design. Motivated by this fact, we construct A-optimal designs for some regression models using a class of algorithms, indexed by a function which depends on the derivatives of the criterion function. We also develop strategies for constructing A-optimal designs and investigate techniques for improving convergence rates by using the properties of the directional derivatives of the criterion function. We explored the design construction through some examples including one practical problem arising in chemistry.