We study a class of decision rules based on an adaptive partitioning of an Euclidean observation space. The class of partitions has a computationally attractive form, and the related decision rule is invariant under strictly monotone transformations of coordinate axes. We provide sufficient conditions that a sequence of decision rules be asymptotically Bayes risk efficient as sample size increases. The sufficient conditions involve no regularity assumptions on the underlying parent distributions.
"Asymptotically Efficient Solutions to the Classification Problem." Ann. Statist. 6 (3) 515 - 533, May, 1978. https://doi.org/10.1214/aos/1176344197