A Note on Minimax Robustness of Designs Against Correlated or Heteroscedastic Responses

TL;DR

This paper demonstrates that certain covariance matrix functions are maximized at scalar multiples of the identity, supporting the robustness of designs optimized for independent, homoscedastic responses against correlated or heteroscedastic alternatives.

Contribution

It establishes a theoretical foundation showing that experimental designs optimal under independence are minimax robust to various covariance structures.

Findings

Designs optimal under independence are robust to correlated responses.

Maximization of covariance functions occurs at scalar multiples of identity matrices.

Supports ignoring dependence or heteroscedasticity in experimental design.

Abstract

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.