Li-Shan Huang (Chair)

Abstract

The usual optimal designs are devised to minimize the variance of the least-squares estimator, although the notion of minimum variance can depend on the specific criterion. Modern regression methods are often biased and hence it is more appropriate to consider a different optimality criterion for optimal design. We tackle this problem by proposing the M-optimal design and use ridge regression as a concrete example. We address technical issues with regard to the practical application and the inference theory for the corresponding estimator based on the M-optimal design. The promising performance of M-optimal design over the usual optimal designs is demonstrated with numerical studies.