Minimax Robust Designs for M-Estimated Models

TL;DR

This paper extends minimax robust experimental design theory from Least Squares to M-estimation, enhancing robustness against outliers and correlation structures.

Contribution

It introduces designs optimized for M-estimation, showing they are asymptotically similar to Least Squares designs with minor tuning adjustments.

Findings

Designs for Least Squares remain optimal asymptotically for M-estimation.

Proposed designs are robust against broad classes of correlation structures.

A minor change in tuning constant suffices for robustness.

Abstract

Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. The theory to date has focussed almost exclusively on Least Squares estimates. Here we extend this theory to designs tailored for M-estimation of parameters, thus obtaining additional robustness against outlying responses. We show that, subject to a minor change in a tuning constant, designs optimal for Least Squares remain so asymptotically for M-estimation. We argue that even this minor change should be ignored, and the tuning constant chosen in an ad hoc but sensible manner which does not depend on which M-estimate is being employed. Our designs and estimates, derived under an assumption of i.i.d. errors, are also shown to be robust, in a minimax sense, against broad classes of correlation structures.