A Concentration of Measure Perspective to Robust Statistics

Cosme Louart, Romain Couillet

Abstract: We provide promising mathematical considerations for the study of robust scatter matrices in the regime where the data number and dimension are large. Chiefly, we present a new realistic model for data with an assumption inspired from the concentration of measure phenomenon. Our technical contribution is to provide a deterministic equivalent for the robust scatter matrix (i) under relaxed assumptions when compared to the robust statistics literature and (ii) with an original proof based on the introduction of a new semi-metric. This brings simultaneously a new methodological approach to robust statistics analysis and a wider application spectrum to more realistic large dimensional data models.