A Robust Maximal F-Ratio Statistic to Detect Clusters Structure

Abstract

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.

Keywords:

• Engelman–Hartigan test statistic
• Maximal F-ratio
• Robustness
• Trimmed k-means

Mathematics Subject Classification:

• Primary 62H30
• Secondary 62F35

Acknowledgments

This research was partially supported by the Spanish Ministerio de Educación y Ciencia and FEDER, grant MTM2008-06067-C02-01 and -02 and the Consejería de Educación y Cultura de la Junta de Castilla y León, GR150.