Mahalanobis’s Fractile Graphs: Some History and New Developments

Mahalanobis’s famous paper on Fractile Graphical Analysis introduced a plethora of new statistical concepts and techniques [see Mahalanobis (1960)]. The method was originally proposed to compare two regression functions. We discuss and re-interpret some of his work, highlighting his contributions and some of the difficulties encountered. We develop a bootstrap based hypothesis test to compare the fractile regression curves based on their isotonized estimators. The proposed procedure does not depend on the choice of any tuning parameter and is computationally simple. Through an extensive simulation study, we illustrate the finite sample performance of our procedure. We also discuss three real data applications that illustrate the scope of the methodology.