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

TL;DR

This paper introduces a method to eliminate points that cannot support E-optimal designs in linear regression, enabling more efficient solutions for large problems via semidefinite programming.

Contribution

It presents a novel point removal technique for E-optimal design problems, extending previous work to more complex criteria and improving computational efficiency.

Findings

Reduces problem size for large E-optimal design problems.

Enables efficient semidefinite programming solutions.

Builds on and extends prior theoretical results.

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.