Removal of the points that do not support an E-optimal experimental design

Abstract

We propose a method of removal of design points that cannot support any E-optimal experimental design of a linear regression model with uncorrelated observations. The proposed method can be used to reduce the size of some large E-optimal design problems such that they can be efficiently solved by semidefinite programming. This paper complements the results of Pronzato [Pronzato, L., 2013. A delimitation of the support of optimal designs for Kiefer's $\phi_p$-class of criteria. Statistics & Probability Letters 83, 2721--2728], who studied the same problem for analytically simpler criteria of design optimality.