Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”

In this discussion, we consider two examples. The first example concerns the Old Faithful data, which the authors (Cerioli, Riani, Atkinson, Corbellini in Stat Methods Appl, to appear) discuss in detail in their paper. The second example, which is taken from www.kaggle.com, is based on the prices and other attributes of 53,900 diamonds. The point of our discussion is to demonstrate that the process of producing valid models and then looking at diagnostics, that compare least squares and robust fits, can also effectively identify outliers and/or important structure missing from the model. Using this approach, we identify a dramatic change point in the diamonds data. We are very curious about what information the sophisticated monitoring methods produce about this change point and its effects on the outcome variable.