Robust Design and Misspecification Detection for Count Models

Résumé fourni par la source

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.

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