Distortion in statistical inference: the distinction between data contamination and model deviation

The present work develops a basic classification scheme for distortion in the framework of classical statistical inference. In particular, it emphasizes the still outstanding and consequent distinction between data contamination and model deviation. It is explored when different implications on the performance of statistical inference procedures under the two types of distortion are possible and how these can be detected. A critical review of some important approaches in the robustness and diagnostics literature finally indicates which of them is aimed at data contamination and which at model deviation (independently from what has been claimed originally). The paper raises awareness of the above problem through a constructive discussion – it is not meant to introduce new methodology