Monotonic convergence of a general algorithm for computing optimal designs

TL;DR

This paper proves that a broad class of multiplicative algorithms for finding optimal experimental designs always converge monotonically, confirming a longstanding conjecture and demonstrating their application to logistic regression.

Contribution

It establishes monotonic convergence for a general class of algorithms and confirms a conjecture, advancing the theoretical understanding of optimal design computation.

Findings

Monotonic convergence is proven for the algorithms.

The conjecture by Titterington is confirmed.

Optimal designs for logistic regression are illustrated.

Abstract

Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379--1389] for computing optimal designs. A conjecture of Titterington [Appl. Stat. 27 (1978) 227--234] is confirmed as a consequence. Optimal designs for logistic regression are used as an illustration.