Hans Nyquist: Fréchet distance as a tool for diagnosing multivariate data

Outliers can have dramatic effects on results from statistical analyses and on conclusions based on statistical analyses. It is therefore important to detect outliers and influential points. In this talk I will discuss how a method based on Fréchet distances can be created for diagnosing outliers. In particular, I will discuss how elements from topology can be used to create a theoretical environment on which statistical methods for this purpose can be based. In the discussion I will also emphasize the importance of originality in the development of new statistical methodology and argue that proofs of theorems may be at least as interesting as the statements made in the theorems.