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Andreas Buja, Richard A. Berk, Arun K. Kuchibhotla, Linda Zhao and Ed George’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes

We thank the authors for their stimulating article. At the highest level, it agrees with our thinking as expressed in the second of two articles in Statistical Science (Buja et al., 2019). The guiding principle is to focus on quantities of interest that are meaningful statistical functionals, beyond the statistical models that motivate them, even when those models are fully misspecified. In some form, this focus has existed for decades in the semiparametric literature. We suggest below a reinterpretation of the authors’ approach and a modification of their third principle.