Seminar Details

Seminar Details


Apr 18

3:30 pm

When is an Outlier Not an Outlier? Connections Between Robust Estimation, Outlier Detection, and False Discovery Rates

Ken Rice


University of Washington - Department of Biostatistics

League tables of performance provide a simple tool for comparison of hospitals, schools, and various other institutions. In typical applications, institutions are assessed by their performance relative to some population average: any institution whose performance is significantly different from this average may be liable to investigation, in order to uncover exceptional behavior.

The assumption of a single acceptable performance rate here is very conservative, and in some cases, up to 70% of institutions are “flagged up” as outliers, even allowing for multiple comparisons. This is plainly ridiculous, and motivates us to study acceptable variation in performance. The approach suggested is to assume a normal distribution for institutions that perform acceptably, and attempt to estimate it allowing for the presence of contaminants. Connections are made between our formal model-based approach and well-known existing robust estimation procedures with more ad hoc derivations. The model-based approach also leads directly to measures of “outlyingness” for each institution; we argue that these can and should be combined using methods from the False Discovery Rate literature. Connections between such methods and Bayesian decision-theoretic approaches are also discussed.