Christian Hennig's contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes
本文讨论了统计中模型假设的误导性表述，指出模型假设不必完全成立，而假设精简方法在更广模型范围内有理论保证，但实际表现仍需检验。
There is a tendency in statistics to talk about model assumptions in a misleading way. Most of us probably agree with George Box's 'all models are wrong but some are useful', yet there is much communication that implies that for applying methods 'assuming' certain models, these models have to be true. If this were so, no model-based method could ever be used! Generally model assumptions do not have to be fulfilled. A model assumption just means that certain theoretical results regarding a statistical procedure hold assuming the model. A procedure may well deliver useful results if its model assumptions do not hold. This can be addressed by investigating what happens if other models hold. The advantage of 'assumption-lean' methods is that they come with theory that applies under a wider range of models, so we know more, but none of this wider range of models will ultimately be 'correct' either, and the theory does not necessarily guarantee a good behaviour in practice.