Asymptotically Efficient Solutions to the Classification Problem

Abstract

We study a class of decision rules based on an adaptive partitioningof an Euclidean observation space. The class of partitions has acomputationally attractive form, and the related decision rule isinvariant under strictly monotone transformations of coordinate axes.We provide sufficient conditions that a sequence of decision rulesbe asymptotically Bayes risk efficient as sample size increases.The sufficient conditions involve no regularity assumptions on theunderlying parent distributions.