Title: On whether to check the model before doing model-based inference
Authors: Christian Hennig - University of Bologna (Italy) [presenting]
Iqbal Shamsudheen - University College London (United Kingdom)
Abstract: Statistical inference comes with model assumptions, and it is a standard recommendation to check the model assumptions before doing model-based inference. A problem with this is that checking model assumptions affects subsequent inference. Even in case a model assumption is in fact fulfilled, it is no longer fulfilled conditionally on passing a model misspecification test (misspecification paradox). In the literature there is some scattered investigation of how big a problem this is, and whether the resulting combined procedures (i.e., choosing the inference method depending on whether certain assumptions are passed or not) are advisable. Much of this work is surprisingly critical of such a practice. Several aspects of such combined procedures are discussed and new results are presented, investigating theoretically and by simulation setups in which fulfilled and violated model assumptions are mixed. This provides a more positive if still not uncritical view of such combined procedures.