On measuring sensitivity to parametric model misspecification
In settings where parametric inference is inconsistent under model misspecification, the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models. To make the comparison tractable, large sample and small misspecification approximations are employed. The ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of sensitivity to model misspecification. The maximum ratio over a family of correct distributions is determined as a measure of worst case sensitivity. As well, the distribution producing this maximum can be examined, to see how a particular combination of a parametric family and estimand is susceptible to model misspecifications.