Locally R-optimal design for Poisson regression model using square-root link function

Abstract

This article obtains locally R-optimal designs for the Poisson regression model using the square-root link function. In the generalized linear model (GLM) configuration, the information matrix is determined by the model’s unknown parameters. In such cases, an experimenter must use the strategy of discovering local optimum designs, which entails first guessing the best value for the parameters and then calculating the optimal designs. The R-optimality criterion has been proposed in the literature as an alternative to the most frequently used D-optimality criterion when the experimenter wishes to minimize the volume of the confidence region for unknown parameters based on Bonferroni t-intervals. The necessary and sufficient conditions of this optimality criterion are verified through the equivalence theorem. All numerical computations were performed using Mathematica 7.0.

Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 157-173.