A Simple Diagnostic Plot Connecting Robust Estimation, Outlier Detection, and False Discovery Rates

Robust estimation of parameters, and identification of specific data points that are discordant with an assumed model, are often treated as different statistical problems. The two aims are, however, closely inter-related and in many cases the two analyses are required simultaneously. We present a simple diagnostic plot that connects existing robust estimators with simultaneous outlier detection, and uses the concept of false discovery rates to allow for the multiple comparisons induced by considering each point as a potential outlier. It is straightforward to implement, and applicable in any situation for which robust estimation procedures exist. Several examples are given.