Inference Robustness vs. Criterion Robustness: An Example

The two distinct concepts of inference and criterion robustness are illustrated with a simple example based on the one-parameter exponential model. The study of inference and criterion robustness of point and interval estimators of the population mean under a more general exponential power model involves simple but fascinating distribution theory. This example could be usefully exploited in elementary mathematical statistics courses, where the topic of robustness is often neglected.