Abstract

Classical optimal designs for count data are highly efficient but degrade

severely when the assumed generalized linear model is misspecified. To address

this, we propose a two-stage robust design framework for Poisson and negative binomial regressions. First, we adapt the nonparametric XICOR correlation

measure to formally detect functional dependence between residuals and design

points. Second, we introduce two robust design criteria—one utilizing pilot data

to target specific deviations, and a minimax-style averaging over a functional class

of misspecifications when prior data are absent. We optimize these non-convex

objective functions using a simulated annealing algorithm. Extensive simulations

and a real-world toxicological application demonstrate that our robust designs

yield substantial efficiency gains over classical approaches under misspecification,

while maintaining low premium costs under correct specification.

Key words and phrases: Generalized linear models, Model misspecification, Op- timal design, Robust statistics

Information

Preprint No.SS-2025-0089
Manuscript IDSS-2025-0089
Complete AuthorsLinglong Kong, Rui Hu, Jordan Slessor
Corresponding AuthorsLinglong Kong
Emailslkong@ualberta.ca

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Acknowledgments

This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) [funding reference number 02589]. Lin-

glong Kong was partially supported by grants from the Canada CIFAR AI

Chairs program, the Alberta Machine Intelligence Institute (AMII), the

Canadian AI Safety Institute Research Program at CIFAR, the Natural

Sciences and Engineering Research Council of Canada (NSERC), NSERC

Alliance - Alberta Innovates Advance Program, and the Canada Research

Chair program from NSERC.

Supplementary Materials

The online supplementary materials contain proofs for Theorems 1, 2, and

  1. Moreover, they contain the detailed algorithmic formulation of the simulated annealing procedure, as well as the results and discussions for the

negative binomial simulations and additional misspecification scenarios.

Supplementary materials are available for download.