A Robust Maximal F-Ratio Statistic to Detect Clusters Structure

A robustified version of the maximal F-ratio considered by Engelman–Hartigan to detect clusters structure is introduced. The robustification follows from the application of an impartial trimming procedure inspired on the trimmed k-means method. Asymptotic results for that trimmed maximal F-ratio are given. These results show that the prize to be paid (in terms of increased asymptotic variance) for the robustification is affordable. An example arising from a genetical study shows the interest of the proposed robustification in applied studies.