Statistical Discrimination Analysis Using the Maximum Function

Abstract

The maximum of k functions defined on R n , n ≥ 1, by f max (x) = max{f 1 (x),…, f k (x)}, ∀ x ∊ R n , can have important roles in Statistics, particularly in Classification. Through its relation with the Bayes error, which is the reference error in classification, it can serve to compute numerical bounds for errors in other classification schemes. It can also serve to define the joint L1-distance between more than two densities, which, in turn, will serve as a useful tool in Classification and Cluster Analyses. It has a vast potential application in digital image processing too. Finally, its versatile role can be seen in several numerical examples, related to the analysis of Fisher's classical iris data in multidimensional spaces.