Efficient Computational Algorithm for Optimal Allocation in Regression Models

TL;DR

This paper introduces a simple, efficient algorithm for optimal experimental design in regression models, proving its convergence and demonstrating its effectiveness through simulations.

Contribution

It provides an alternative proof of convergence for a $D$-optimality algorithm and proposes a new algorithm with conjectured convergence for $A$-optimality.

Findings

The $D$-algorithm converges monotonically to the optimal solution.

Monte Carlo simulations confirm the algorithm's reliability and efficiency.

The proposed methods improve computational performance in optimal design problems.

Abstract

In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been discussed in the literature. Here, we provide an alternate proof of the monotonic convergence for $D$-criterion with a simple computational algorithm and furthermore show it converges to the $D$-optimality. We also discuss an algorithm as well as a conjecture of the monotonic convergence for $A$-criterion. Monte Carlo simulations are used to demonstrate the reliability, efficiency and usefulness of the proposed algorithms.