# Comparing robustness properties of optimal designs under standard and compound criteria

## TL;DR

This paper compares the robustness of optimal experimental designs based on standard, modified, and compound criteria, especially considering the impact of estimated error variance on design optimality.

## Contribution

It introduces a comparison framework for different optimality criteria, including compound criteria, and evaluates their robustness in factorial design settings.

## Key findings

- Compound criteria can lead to more robust designs.
- Modified criteria account for error variance estimation.
- Standard criteria may produce less robust designs.

## Abstract

Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have been commonly used for obtaining optimal designs. For a given statistical model, standard criteria assume the error variance is known at the design stage. However, in practice the error variance is estimated to make inference about the model parameters. Modified criteria are defined as a function of the standard criteria and the corresponding error degrees of freedom, which may lead to extreme optimal design. Compound criteria are defined as the function of different modified criteria and corresponding user specified weights. Standard, modified, and compound criteria based optimal designs are obtained for $3^3$ factorial design. Robustness properties of the optimal designs are also compared.