A Concentration of Measure Perspective to Robust Statistics
Résumé
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.